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Professor Wadim Zudilin

Professor

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Research Expertise
(listed below in obscure alphabetical order) Apéry's theorem Calabi–Yau differential equations Dilogarithm Diophantine approximations Diophantine equations Experimental Mathematics Hypergeometric series Irrationality and transcendence L-values Mahler measures Mathematical constants Mock theta functions Modular forms and functions Multiple zeta values Number Theory in general Ordinary zeta values Orthogonal polynomials Padé approximations Pi = 3.14159265358979323846264338327950288419716939937510... Positivity Ramanujan's mathematics Rogers–Ramanujan identities Special functions Supercongruences

Qualifications

  • Diploma of the Candidate in Sciences, Lomonosov Moscow State University

Keywords

  • algebra
  • analysis
  • differential equations
  • number theory
  • special functions

Fields of Research

Code Description Percentage
010299 Applied Mathematics not elsewhere classified 10
090699 Electrical and Electronic Engineering not elsewhere classified 5
010199 Pure Mathematics not elsewhere classified 85

Professional Experience

UON Appointment

Title Organisation / Department
Professor University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/01/2008 - 1/12/2009 Fellowship Max Planck Society
Germany
1/01/2007 - 1/12/2007 Fellowship Max Planck Society
Germany
1/01/2006 - 1/12/2006 Fellowship

Research Fellowship

Max Planck Society
Germany
1/01/2003 -  Fellowship Alexander Von Humboldt Foundation
Germany
1/01/2000 - 1/01/2003 Fellowship Russian Academy of Sciences
Russian Federation
1/01/1999 -  Fellowship

Post Doctoral Fellowship

Ostrowski Foundation
Switzerland

Awards

Recipient

Year Award
2006 Competition of the Talented Students, Graduates & Young Scientists of the Moscow University
Unknown
2001 The Distinguished Award of the Hardy-Ramanujan Society
Unknown
1997 Young Scientists' Competition
Unknown
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (3 outputs)

Year Citation Altmetrics Link
2014 Borwein J, Poorten AVD, Shallit J, Zudilin W, Neverending Fractions, Cambridge University Press, Cambridge, U.K., 224 (2014) [A2]
Co-authors Jonathan Borwein
2014 Borwein J, Poorten AVD, Shallit J, Zudilin W, Neverending Fractions, Cambridge University Press, Cambridge, U.K., 224 (2014) [A2]
Co-authors Jonathan Borwein
2013 Borwein JM, Shparlinski I, Zudilin W, Number Theory and Related Fields: In Memory of Alf van der Poorten, Springer New York LLC (2013) [A3]
DOI 10.1007/978-1-4614-6642-0
Co-authors Jonathan Borwein

Chapter (4 outputs)

Year Citation Altmetrics Link
2013 Zudilin W, 'Period(d)ness of L-Values', Number Theory and Related Fields, Springer, New York 381-395 (2013) [B1]
DOI 10.1007/978-1-4614-6642-0_20
2013 Chappell T, Lascoux A, Warnaar SO, Zudilin V, 'Logarithmic and complex constant term identities', Computational and Analytical Mathematics, Springer, New York 219-250 (2013) [B1]
DOI 10.1007/978-1-4614-7621-4_11
2013 Zudilin W, 'Lost in Translation', Advances in Combinatorics, Springer, Berlin 287-293 (2013) [B1]
DOI 10.1007/978-3-642-30979-3_16
2013 Guillera J, Zudilin V, 'Ramanujan-type formulae for 1/p: The art of translation', The Legacy of Srinivasa Ramanujan, Ramanujan Mathematical Society, India 181-195 (2013) [B1]
Show 1 more chapter

Journal article (84 outputs)

Year Citation Altmetrics Link
2015 Zudilin W, 'On three theorems of Folsom, Ono and Rhoades', Proceedings of the American Mathematical Society, 143 1471-1476 (2015)

In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotic matches the one of a modular form, though ... [more]

In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotic matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom, Ono and Rhoades have proved an elegant result about the match for a general family related to Dyson¿s rank (mock theta) function and the Andrews¿Garvan crank (modular) function¿ the match with explicit formulae for implied O(1) constants. In this note we give another elementary proof of Ramanujan¿s original claim and outline some heuristics which may be useful for obtaining a new proof of the general Folsom¿Ono¿Rhoades theorem.

DOI 10.1090/S0002-9939-2014-12364-1
2015 Osburn R, Zudilin W, 'On the (K.2) supercongruence of Van Hamme', Journal of Mathematical Analysis and Applications, (2015)
DOI 10.1016/j.jmaa.2015.08.009
2015 Viola C, Zudilin W, 'Linear independence of dilogarithmic values', Journal für die reine und angewandte Mathematik (Crelles Journal), 0 (2015)
DOI 10.1515/crelle-2015-0030
2015 Brent RP, Coons M, Zudilin W, 'Algebraic Independence of Mahler Functions via Radial Asymptotics', International Mathematics Research Notices, (2015)
DOI 10.1093/imrn/rnv139
Co-authors Michael Coons
2015 Zudilin W, 'Multiple q-Zeta Brackets', Mathematics, 3 119-130 (2015)
DOI 10.3390/math3010119
2014 Zudilin W, 'A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 89 125-131 (2014) [C1]
DOI 10.1017/S0004972713000233
2014 Straub A, Zudilin W, 'Positivity of rational functions and their diagonals', Journal of Approximation Theory, (2014)

The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szego{double acu... [more]

The problem to decide whether a given rational function in several variables is positive, in the sense that all its Taylor coefficients are positive, goes back to Szego{double acute} as well as Askey and Gasper, who inspired more recent work. It is well known that the diagonal coefficients of rational functions are D-finite. This note is motivated by the observation that, for several of the rational functions whose positivity has received special attention, the diagonal terms in fact have arithmetic significance and arise from differential equations that have modular parametrization. In each of these cases, this allows us to conclude that the diagonal is positive. Further inspired by a result of Gillis, Reznick and Zeilberger, we investigate the relation between positivity of a rational function and the positivity of its diagonal. Crown Copyright © 2014.

DOI 10.1016/j.jat.2014.05.012
Citations Scopus - 1
2014 Dauguet S, Zudilin W, 'On simultaneous diophantine approximations to ¿(2) and ¿(3)', Journal of Number Theory, 145 362-387 (2014) [C1]

We present a hypergeometric construction of rational approximations to ¿(2) and ¿(3) which allows one to demonstrate simultaneously the irrationality of each of the zeta values,... [more]

We present a hypergeometric construction of rational approximations to ¿(2) and ¿(3) which allows one to demonstrate simultaneously the irrationality of each of the zeta values, as well as to estimate from below certain linear forms in 1, ¿(2) and ¿(3) with rational coefficients. We then go further to formalize the arithmetic structure of these specific linear forms by introducing a new notion of (simultaneous) diophantine exponent. Finally, we study the properties of this newer concept and link it to the classical irrationality exponent and its generalizations given recently by S. Fischler. © 2014 Elsevier Inc.

DOI 10.1016/j.jnt.2014.06.007
Citations Scopus - 1Web of Science - 1
2014 Zudilin W, 'Regulator of modular units and Mahler measures', Mathematical Proceedings of the Cambridge Philosophical Society, 156 313-326 (2014) [C1]
DOI 10.1017/S0305004113000765
Citations Web of Science - 1
2014 Rogers M, Zudilin W, 'On the Mahler Measure of 1+X+1/X+Y +1/Y', International Mathematics Research Notices, 2014 2305-2326 (2014) [C1]
DOI 10.1093/imrn/rns285
Citations Scopus - 2Web of Science - 3
2014 Zudilin W, 'Two hypergeometric tales and a new irrationality measure of ¿(2)', Annales mathématiques du Québec, 38 101-117 (2014) [C1]
DOI 10.1007/s40316-014-0016-0
2013 Chan HH, Wan J, Zudilin W, 'Legendre polynomials and Ramanujan-type series for 1/p', Israel Journal of Mathematics, 194 183-207 (2013) [C1]
DOI 10.1007/s11856-012-0081-5
Citations Scopus - 5Web of Science - 5
2013 Wan J, Zudilin W, 'Generating functions of Legendre polynomials: A tribute to Fred Brafman', Journal of Approximation Theory, 170 198-213 (2013) [C1]
DOI 10.1016/j.jat.2012.11.001
Citations Scopus - 2Web of Science - 2
2013 Zudilin V, 'On the irrationality measure of p^2', Russian Mathematical Surveys, 68 1133-1135 (2013) [C1]
DOI 10.1070/RM2013v068n06ABEH004872
Citations Web of Science - 1
2012 Guillera J, Zudilin V, ''Divergent' Ramanujan-type supercongruences', Proceedings of the American Mathematical Society, 140 765-777 (2012) [C1]
Citations Scopus - 6Web of Science - 5
2012 Borwein JM, Straub A, Wan G, Zudilin V, 'Densities of short uniform random walks', Canadian Journal of Mathematics, 64 961-990 (2012) [C1]
DOI 10.4153/CJM-2011-079-2
Citations Scopus - 10Web of Science - 9
Co-authors Jonathan Borwein
2012 Rogers M, Zudilin V, 'From L-series of elliptic curves to Mahler measures', Compositio Mathematica, 148 385-414 (2012) [C1]
Citations Scopus - 8Web of Science - 10
2012 Wan G, Zudilin V, 'Generating functions of Legendre polynomials: A tribute to Fred Brafman', Journal of Approximation Theory, 164 488-503 (2012) [C1]
Citations Scopus - 5Web of Science - 5
2012 Ohno Y, Okuda J-I, Zudilin V, 'Cyclic q-MZSV sum', Journal of Number Theory, 132 144-155 (2012) [C1]
Citations Scopus - 3Web of Science - 4
2012 Warnaar SO, Zudilin V, 'Dedekind's ¿-function and Rogers-Ramanujan identities', Bulletin of the London Mathematical Society, 44 1-11 (2012) [C1]
Citations Scopus - 6Web of Science - 6
2012 Chan HH, Wan G, Zudilin V, 'Complex series for 1/p', Ramanujan Journal, 29 135-144 (2012) [C1]
Citations Scopus - 1
2011 Chan HH, Tanigawa Y, Yang Y, Zudilin V, 'New analogues of Clausen's identities arising from the theory of modular forms', Advances in Mathematics, 228 1294-1314 (2011) [C1]
DOI 10.1016/j.aim.2011.06.011
Citations Scopus - 11Web of Science - 10
2011 Warnaar SO, Zudilin V, 'A q-rious positivity', Aequationes Mathematicae, 81 177-183 (2011) [C1]
DOI 10.1007/s00010-010-0055-9
Citations Scopus - 4Web of Science - 5
2011 Almkvist G, Van Straten D, Zudilin V, 'Generalizations of Clausen's Formula and algebraic transformations of Calabi-Yau differential equations', Proceedings of the Edinburgh Mathematical Society, 54 273-295 (2011) [C1]
DOI 10.1017/S0013091509000959
Citations Scopus - 9Web of Science - 9
2011 Zudilin V, 'Book Review: Ramanujan's Lost Notebook. Part II, G.E. Andrews, B.C. Berndt', Journal of Approximation Theory, 163 1037-1038 (2011) [C3]
2011 Gallot Y, Moree P, Zudilin V, 'The Erd's-Moser equation 1k +2k +...+(m-1)k = mk revisited using continued fractions', Mathematics of Computation, 80 1221-1237 (2011) [C1]
Citations Scopus - 4Web of Science - 4
2011 Zudilin V, 'Arithmetic hypergeometric series', Russian Mathematical Surveys, 66 369-420 (2011) [C1]
DOI 10.1070/RM2011v066n02ABEH004742
Citations Scopus - 8Web of Science - 4
2010 Chan HH, Long L, Zudilin V, 'A supercongruence motivated by the Legendre family of elliptic curves', Mathematical Notes, 88 599-602 (2010) [C1]
DOI 10.1134/S0001434610090324
Citations Scopus - 2Web of Science - 1
2010 Chan HH, Zudilin V, 'New representations for apery-like sequences', Mathematika, 56 107-117 (2010) [C1]
DOI 10.1112/s0025579309000436
Citations Scopus - 10Web of Science - 10
2010 Fischler S, Zudilin V, 'A refinement of Nesterenko's linear independence criterion with applications to zeta values', Mathematische Annalen, 347 739-763 (2010) [C1]
DOI 10.1007/s00208-009-0457-y
Citations Scopus - 5Web of Science - 5
2010 Bailey DH, Borwein JM, Broadhurst D, Zudilin V, 'Experimental mathematics and mathematical physics', Contemporary Mathematics, 517 41-58 (2010) [C1]
Citations Web of Science - 3
Co-authors Jonathan Borwein
2010 Yang Y, Zudilin V, 'On Sp4 modularity of Picard-Fuchs differential equations for Calabi-Yan threefolds', Contemporary Mathematics, 517 381-413 (2010) [C1]
DOI 10.1090/conm/517
2009 Zudilin V, 'Apery's theorem. Thirty years after', International Journal of Mathematics and Computer Science, 4 9-19 (2009) [C1]
2009 Zudilin V, 'Ramanujan-type supercongruences', Journal of Number Theory, 129 1848-1857 (2009) [C1]
DOI 10.1016/j.jnt.2009.01.01
Citations Scopus - 10Web of Science - 11
2009 Krattenthaler C, Rochev I, Vaananen K, Zudilin V, 'On the non-quadraticity of values of the q-exponential function and related q-series', Acta Arithmetica, 136 243-269 (2009) [C1]
DOI 10.4064/aa136-3-4
Citations Scopus - 2Web of Science - 2
2009 Zudilin V, 'A hypergeometric problem', Journal of Computational and Applied Mathematics, 233 856-857 (2009) [C1]
DOI 10.1016/j.cam.2009.02.053
2008 Ohno Y, Zudilin W, 'Zeta Stars', Communications in Number Theory and Physics, 2 325-347 (2008) [C1]
Citations Scopus - 21Web of Science - 16
2008 Zudilin W, 'Linear independence of values of Tschakaloff functions with different parameters', Journal of Number Theory, 128 2549-2558 (2008) [C1]
DOI 10.1016/j.jnt.2008.03.003
Citations Scopus - 2Web of Science - 2
2008 Viola C, Zudilin W, 'Hypergeometric transformations of linear forms in one logarithm', Functiones et Approximatio Commentarii Mathematici, 39 211-222 (2008) [C1]
2007 Zudilin W, 'Approximations to -, di- and tri-logarithms', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 202 450-459 (2007) [C1]
DOI 10.1016/j.cam.2005.04.076
Citations Scopus - 4Web of Science - 4
2007 Zudilin W, 'An elementary proof of the irrationality of Tschakaloff series', Journal of Mathematical Sciences, 146 5669-5673 (2007) [C1]
DOI 10.1007/s10958-007-0382-0
2007 Zudilin W, 'A new lower bound for II(3/2)kII', Journal de Theorie des Nombres de Bordeaux, 19 313-325 (2007) [C1]
2007 Zudilin VV, 'Quadratic transformations and Guillera's formulas for 1/pi(2)', MATHEMATICAL NOTES, 81 297-301 (2007) [C1]
DOI 10.1134/S0001434607030030
Citations Scopus - 5Web of Science - 4
2007 Bundschuh P, Zudilin W, 'Irrationality measures for certain q-mathematical constants', MATHEMATICA SCANDINAVICA, 101 104-122 (2007) [C1]
Citations Scopus - 8Web of Science - 7
2007 Vaananen K, Zudilin WV, 'Linear independence of values of Tschakaloff series', RUSSIAN MATHEMATICAL SURVEYS, 62 196-198 (2007) [C1]
DOI 10.1070/RM2007v062n01ABEH004386
Citations Scopus - 1
2007 Zudilin VV, 'More Ramanujan-type formulae for 1/p 2', Russian Mathematical Surveys, 62 634-636 (2007) [C1]
DOI 10.1070/RM2007v062n03ABEH004420
Citations Scopus - 7
2006 Matala-Aho T, Vaananen K, Zudilin W, 'New irrationality measures for q-logarithms', MATHEMATICS OF COMPUTATION, 75 879-889 (2006) [C1]
Citations Scopus - 10Web of Science - 9
2006 Pilehrood KH, Pilehrood TH, Zudilin W, 'Irrationality of certain numbers that contain values of the di- and trilogarithm', MATHEMATISCHE ZEITSCHRIFT, 254 299-313 (2006) [C1]
DOI 10.1007/s00209-006-0948-4
Citations Scopus - 1Web of Science - 1
2006 Sondow J, Zudilin W, 'Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper', RAMANUJAN JOURNAL, 12 225-244 (2006) [C1]
DOI 10.1007/s11139-006-0075-1
Citations Scopus - 8Web of Science - 9
2006 Krattenthaler C, Rivoal T, Zudilin W, 'Series hypergeometriques basiques, q-analogues des valeurs de la fonction zeta et formes modulaires', Journal of the Institute of Mathematics of Jussieu, 5 53-79 (2006) [C1]
2006 Zudilin W, 'Approximations to q-logarithms and q-dilogarithms, with applications to q-zeta values', Journal of Mathematical Sciences, 137 4673-4683 (2006) [C1]

We construct simultaneous rational approximations to q-series L 1(x1; q) and L1(x2; q) and, if x = x1 = x2, to series L1(x; q) and L 2(x; q), where L1 (x;q) = ¿8n=1(xq) n/1-qn=¿... [more]

We construct simultaneous rational approximations to q-series L 1(x1; q) and L1(x2; q) and, if x = x1 = x2, to series L1(x; q) and L 2(x; q), where L1 (x;q) = ¿8n=1(xq) n/1-qn=¿8n=1xqn/1-xqn L2 (x;q) = ¿8n=1n(xq)n/1-qn= ¿8n=1xqn/1-xqn. Applying the construction, we obtain quantitative linear independence over Q of the numbers in the following collections: 1, ¿q(1) = L1(1; q), ¿ (q 2) and 1, ¿q(1), ¿q(2) = L 2(1; q) for q = 1/p, p e Z \ (0,±1). Bibliography: 14 titles. © 2006 Springer Science+Business Media, Inc.

DOI 10.1007/s10958-006-0263-y
Citations Scopus - 3
2005 Vaananen K, Zudilin W, 'Baker-type estimates for linear forms in the values of q-series', CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 48 147-160 (2005) [C1]
DOI 10.4153/CMB-2005-013-5
Citations Scopus - 3Web of Science - 3
2005 Zudilin W, 'Well-poised generation of Apery-like recursions', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 178 513-521 (2005) [C1]
DOI 10.1016/j.cam.2003.11.016
Citations Web of Science - 1
2005 Zudilin WV, 'Ramanujan-type formulae and irrationality measures of some multiples of p', Sbornik Mathematics, 196 983-998 (2005)
DOI 10.1070/SM2005v196n07ABEH000945
Citations Scopus - 1
2005 Zudilin W, 'Computing powers of two generalizations of the logarithm', Seminaire Lotharingien de Combinatoire, 53 1-6 (2005) [C1]
2004 Zudilin VV, 'Binomial sums related to rational approximations to ¿(4)', Mathematical Notes, 75 594-597 (2004)
Citations Scopus - 2
2004 Zudilin VV, 'The inverse legendre transform of a certain family of sequences', Mathematical Notes, 76 276-279 (2004) [C1]
DOI 10.1023/B:MATN.0000036764.72552.55
Citations Scopus - 1
2004 Zudilin W, 'Binomial sums related to rational approximations to Zeta(4)', Russian Academy of Sciences: Mathematical Notes, 75 594-597 (2004) [C1]
DOI 10.1023/B:MATN.0000023341.93824.fb
2004 Bundschuh P, Zudilin W, 'On theorems of Gelfond and Selberg concerning integral-valued entire functions', JOURNAL OF APPROXIMATION THEORY, 130 164-178 (2004) [C1]
DOI 10.1016/j.jat.2004.07.005
Citations Scopus - 5Web of Science - 5
2004 Zudilin W, 'Well-poised hypergeometric transformations of Euler-type multiple integrals', JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 70 215-230 (2004) [C1]
DOI 10.1112/S0024610704005472
Citations Scopus - 5Web of Science - 6
2004 Zudilin W, 'Heine's basic transform and a permutation group for q-harmonic series', ACTA ARITHMETICA, 111 153-164 (2004) [C1]
DOI 10.4064/aa111-2-4
Citations Scopus - 13Web of Science - 10
2004 Zudilin W, 'On a combinatorial problem of Asmus Schmidt', ELECTRONIC JOURNAL OF COMBINATORICS, 11 (2004) [C1]
Citations Web of Science - 5
2004 Zudilin W, 'On a combinatorial problem of Asmus Schmidt', Electronic Journal of Combinatorics, 11 (2004)
Citations Scopus - 7
2004 Zudilin W, 'Arithmetic of linear forms involving odd zeta values', Journal de Theorie des Nombres de Bordeaux, 16 251-291 (2004) [C1]
DOI 10.5802/jtnb.447
2003 Zudilin W, 'The hypergeometric equation and Ramanujan functions', RAMANUJAN JOURNAL, 7 435-447 (2003) [C1]
DOI 10.1023/B:RAMA.0000012426.23921.24
Citations Scopus - 7Web of Science - 7
2003 Zudilin VV, 'On the Functional Transcendence of q-Zeta Values', Mathematical Notes, 73 588-589 (2003) [C1]
DOI 10.1023/A:1023275708583
Citations Scopus - 1
2003 Rivoal T, Zudilin W, 'Diophantine properties of numbers related to Catalan's constant', MATHEMATISCHE ANNALEN, 326 705-721 (2003) [C1]
DOI 10.1007/s00208-003-0420-2
Citations Scopus - 20Web of Science - 18
2003 Zudilin VV, 'Algebraic relations for multiple zeta values', Russian Mathematical Surveys, 58 1-29 (2003) [C1]
DOI 10.1070/RM2003v058n01ABEH000592
Citations Scopus - 16
2003 Bertrand D, Zudilin W, 'On the transcendence degree, of the differential field generated by Siegel modular forms', JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 554 47-68 (2003) [C1]
Citations Web of Science - 4
2003 Zudilin W, 'An Apery-like difference equation for Catalan's constant', ELECTRONIC JOURNAL OF COMBINATORICS, 10 (2003) [C1]
Citations Web of Science - 7
2003 Zudilin W, 'An Apéry-like difference equation for Catalan's constant', Electronic Journal of Combinatorics, 10 (2003)

Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan's constant with rational co... [more]

Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan's constant with rational coefficients, we obtain a second-order difference equation for these forms and their coefficients. As a consequence we derive a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it. Similar arguments are put forward to deduce a second-order difference equation and a new continued fraction for ¿(4) = p4/90.

Citations Scopus - 6
2003 Zudilin W, 'Well-poised hypergeometric service for diophantine problems of zeta values', Journal de Theorie des Nombres de Bordeaux, 15 593-626 (2003) [C1]
DOI 10.5802/jtnb.415
2002 Zudilin W, 'Remarks on irrationality of q-harmonic series', MANUSCRIPTA MATHEMATICA, 107 463-477 (2002)
DOI 10.1007/s002290200249
Citations Scopus - 8Web of Science - 6
2002 Zudilin VV, 'Very well-poised hypergeometric series and multiple integrals', Russian Mathematical Surveys, 57 824-826 (2002)
DOI 10.1070/RM2002v057n04ABEH000542
Citations Scopus - 4
2002 Zudilin WV, 'On the irrationality measure for a q-analogue of ¿(2)', Sbornik Mathematics, 193 1151-1172 (2002)
Citations Scopus - 6
2002 Zudilin W, 'Irrationality of values of the Riemann zeta function', Izvestiya Mathematics, 66 489-542 (2002)

The paper deals with a generalization of Rivoal's construction, which enables one to construct linear approximating forms in 1 and the values of the zeta function ¿(s) only at od... [more]

The paper deals with a generalization of Rivoal's construction, which enables one to construct linear approximating forms in 1 and the values of the zeta function ¿(s) only at odd points. We prove theorems on the irrationality of the number ¿(s) for some odd integers s in a given segment of the set of positive integers. Using certain refined arithmetical estimates, we strengthen Rivoal's original results on the linear independence of the ¿(s). © 2002 RAS(DoM) and LMS.

DOI 10.1070/IM2002v066n03ABEH000387
Citations Scopus - 8
2002 Zudilin VV, 'Integrality of power expansions related to hypergeometric series', Mathematical Notes, 71 604-616 (2002)

In the present paper, we study the arithmetic properties of power expansions related to generalized hypergeometric differential equations and series. Defining the series f(z), g(z... [more]

In the present paper, we study the arithmetic properties of power expansions related to generalized hypergeometric differential equations and series. Defining the series f(z), g(z) in powers of z so that f(z) and f(z) log z + g(z) satisfy a hypergeometric equation under a special choice of parameters, we prove that the series q(z) = ze g(Cz)/f(Cz) in powers of z and its inversion z(q) in powers of q have integer coefficients (here the constant C depends on the parameters of the hypergeometric equation). The existence of an integral expansion z(q) for differential equations of second and third order is a classical result; for orders higher than 3 some partial results were recently established by Lian and Yau. In our proof we generalize the scheme of their arguments by using Dwork's p-adic technique.

DOI 10.1023/A:1015827602930
Citations Scopus - 6
2002 Zudilin VV, 'A third-order Apéry-like recursion for ¿(5)', Mathematical Notes, 72 733-737 (2002)
DOI 10.1023/A:1021473409544
Citations Scopus - 4
2002 Zudilin VV, 'Diophantine problems for q-Zeta values', Mathematical Notes, 72 858-862 (2002)
DOI 10.1023/A:1021450231834
Citations Scopus - 5
2001 Zudilin VV, 'One of the eight numbers ¿(5), ¿(7),¿ , ¿(17), ¿(19) is irrational', Mathematical Notes, 70 426-431 (2001)
Citations Scopus - 1
2001 Bertrand D, Zudilin W, 'Derivatives of Siegel modular forms and exponential functions', Izvestiya Mathematics, 65 659-671 (2001)

We show that the differential field generated by Siegel modular forms and the differential field generated by exponentials of polynomials are linearly disjoint over C. Combined wi... [more]

We show that the differential field generated by Siegel modular forms and the differential field generated by exponentials of polynomials are linearly disjoint over C. Combined with our previous work [3], this provides a complete multidimensional extension of Mahler's theorem on the transcendence degree of the field generated by the exponential function and the derivatives of a modular function. We give two proofs of our result, one purely algebraic, the other analytic, but both based on arguments from differential algebra and on the stability under the action of the symplectic group of the differential field generated by rational and modular functions. ©2001 RAS(DoM) and LMS.

DOI 10.1070/IM2001v065n04ABEH000345
Citations Scopus - 1
1997 Zudilin VV, 'On the measure of linear and algebraic independence for values of entire hypergeometric functions', Mathematical Notes, 61 246-248 (1997)
1997 Zudilin VV, 'Recurrent sequences and the measure of irrationality of values of elliptic integrals', Mathematical Notes, 61 657-661 (1997)
1996 Zudilin VV, 'On the algebraic structure of functional matrices of special form', Mathematical Notes, 60 642-648 (1996)
Show 81 more journal articles

Conference (5 outputs)

Year Citation Altmetrics Link
2008 Almkvist G, Van Straten D, Zudilin W, 'Apery limits of differential equations of order 4 and 5', Modular Forms and String Duality - Fields Institute Communications, Banff, Canada (2008) [E1]
2008 Zudilin W, 'Ramanujan-type formulae for 1/p: A second wind?', Modular Forms and String Duality - Fields Institute Communications, Banff, Canada (2008) [E1]
Citations Web of Science - 20
2008 Bundschuh P, Zudilin W, 'Rational approximations to a q-analogue of p and some other q-series', Diophantine Approximation, Vienna, Austria (2008) [E1]
Citations Scopus - 1
2007 Zudilin WV, 'More Ramanujan-type formulae for 1/pi(2)', RUSSIAN MATHEMATICAL SURVEYS, Steklov Math Inst, Moscow, RUSSIA (2007)
DOI 10.1070/RM2007v062n03ABEH004420.
Citations Web of Science - 10
2006 Almkvist G, Zudilin W, 'Differential equations, mirror maps and zeta values', Mirror Symmetry V, Banff, Canada (2006) [E1]
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Grants and Funding

Summary

Number of grants 2
Total funding $330,000

Click on a grant title below to expand the full details for that specific grant.


20141 grants / $75,000

Elliptical special functions$75,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor Ole Warnaar, Professor Wadim Zudilin
Scheme Discovery Projects
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1301362
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20111 grants / $255,000

Arithmetic hypergeometric series$255,000

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Professor Wadim Zudilin
Scheme Discovery Projects
Role Lead
Funding Start 2011
Funding Finish 2011
GNo G1000167
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y
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Research Supervision

Number of supervisions

Completed5
Current0

Past Supervision

Year Level of Study Research Title / Program / Supervisor Type
2015 PhD Arithmetic Applications of Hankel Determinants
Mathematics, Faculty of Science and Information Technology, The University of Newcastle
Co-Supervisor
2013 PhD Random Walks, Elliptic Integrals and Related Constants
Mathematics, Faculty of Science and Information Technology, The University of Newcastle
Co-Supervisor
2011 PhD 'Arithmetic applications of the theory of hypergeometric series'
Math Sc Not Elsewhere Classifi, Unknown
Principal Supervisor
2011 PhD 'Arithmetic properties of the values of certain analytical functions'
Math Sc Not Elsewhere Classifi, Unknown
Principal Supervisor
2007 PhD Ramanujan's Series: Generalizations and Conjectures'
Math Sc Not Elsewhere Classifi, Unknown
Principal Supervisor
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Professor Wadim Zudilin

Position

Professor
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Email wadim.zudilin@newcastle.edu.au
Phone (02)4921 5530
Fax (02)4921 6898

Office

Room 236
Building V
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