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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

CodeDescriptionPercentage
010299Applied Mathematics not elsewhere classified10
090699Electrical and Electronic Engineering not elsewhere classified5
010199Pure Mathematics not elsewhere classified85

Professional Experience

UON Appointment

DatesTitleOrganisation / Department
1/01/2014 - ProfessorUniversity of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

DatesTitleOrganisation / Department
1/01/2008 - 1/12/2009FellowshipMax Planck Society
Germany
1/01/2007 - 1/12/2007FellowshipMax Planck Society
Germany
1/01/2006 - 1/12/2006Fellowship
Research Fellowship
Max Planck Society
Germany
1/01/2003 - FellowshipAlexander Von Humboldt Foundation
Germany
1/01/2000 - 1/01/2003FellowshipRussian Academy of Sciences
Russian Federation
1/01/1999 - Fellowship
Post Doctoral Fellowship
Ostrowski Foundation
Switzerland

Awards

Recipient

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

Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (3 outputs)

YearCitationAltmetricsLink
2014Borwein J, Poorten AVD, Shallit J, Zudilin W, Neverending Fractions, Cambridge University Press, Cambridge, U.K., 224 (2014) [A2]
Co-authorsJonathan Borwein
2014Borwein J, Poorten AVD, Shallit J, Zudilin W, Neverending Fractions, Cambridge University Press, Cambridge, U.K., 224 (2014) [A2]
Co-authorsJonathan Borwein
2013Borwein JM, Shparlinski I, Zudilin W, Number Theory and Related Fields: In Memory of Alf van der Poorten, Springer New York LLC (2013) [A3]
DOI10.1007/978-1-4614-6642-0
Co-authorsJonathan Borwein

Chapter (4 outputs)

YearCitationAltmetricsLink
2013Zudilin W, 'Period(d)ness of L-Values', Number Theory and Related Fields, Springer, New York 381-395 (2013) [B1]
DOI10.1007/978-1-4614-6642-0_20Author URL
2013Chappell T, Lascoux A, Warnaar SO, Zudilin V, 'Logarithmic and complex constant term identities', Computational and Analytical Mathematics, Springer, New York 219-250 (2013) [B1]
DOI10.1007/978-1-4614-7621-4_11
2013Zudilin W, 'Lost in Translation', Advances in Combinatorics, Springer, Berlin 287-293 (2013) [B1]
DOI10.1007/978-3-642-30979-3_16
2013Guillera 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]
Author URL
Show 1 more chapter

Journal article (80 outputs)

YearCitationAltmetricsLink
2015Zudilin 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 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.

DOI10.1090/S0002-9939-2014-12364-1
2014Zudilin W, 'A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 89 125-131 (2014) [C1]
DOI10.1017/S0004972713000233Author URL
2014Straub 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 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.

DOI10.1016/j.jat.2014.05.012
CitationsScopus - 1
2014Dauguet 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, 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.

DOI10.1016/j.jnt.2014.06.007
CitationsScopus - 1Web of Science - 1
2014Zudilin W, 'Regulator of modular units and Mahler measures', Mathematical Proceedings of the Cambridge Philosophical Society, 156 313-326 (2014) [C1]
DOI10.1017/S0305004113000765Author URL
CitationsWeb of Science - 1
2014Rogers M, Zudilin W, 'On the Mahler Measure of 1+X+1/X+Y +1/Y', International Mathematics Research Notices, 2014 2305-2326 (2014) [C1]
DOI10.1093/imrn/rns285
CitationsScopus - 2Web of Science - 3
2014Zudilin W, 'Two hypergeometric tales and a new irrationality measure of ¿(2)', Annales mathématiques du Québec, 38 101-117 (2014) [C1]
DOI10.1007/s40316-014-0016-0
2013Chan HH, Wan J, Zudilin W, 'Legendre polynomials and Ramanujan-type series for 1/p', Israel Journal of Mathematics, 194 183-207 (2013) [C1]
DOI10.1007/s11856-012-0081-5Author URL
CitationsScopus - 5Web of Science - 5
2013Wan J, Zudilin W, 'Generating functions of Legendre polynomials: A tribute to Fred Brafman', Journal of Approximation Theory, 170 198-213 (2013) [C1]
DOI10.1016/j.jat.2012.11.001Author URL
CitationsScopus - 2Web of Science - 2
2013Zudilin V, 'On the irrationality measure of p^2', Russian Mathematical Surveys, 68 1133-1135 (2013) [C1]
DOI10.1070/RM2013v068n06ABEH004872
CitationsWeb of Science - 1
2012Guillera J, Zudilin V, ''Divergent' Ramanujan-type supercongruences', Proceedings of the American Mathematical Society, 140 765-777 (2012) [C1]
CitationsScopus - 6Web of Science - 5
2012Borwein JM, Straub A, Wan G, Zudilin V, 'Densities of short uniform random walks', Canadian Journal of Mathematics, 64 961-990 (2012) [C1]
DOI10.4153/CJM-2011-079-2
CitationsScopus - 10Web of Science - 9
Co-authorsJonathan Borwein
2012Rogers M, Zudilin V, 'From L-series of elliptic curves to Mahler measures', Compositio Mathematica, 148 385-414 (2012) [C1]
CitationsScopus - 8Web of Science - 10
2012Wan G, Zudilin V, 'Generating functions of Legendre polynomials: A tribute to Fred Brafman', Journal of Approximation Theory, 164 488-503 (2012) [C1]
CitationsScopus - 5Web of Science - 5
2012Ohno Y, Okuda J-I, Zudilin V, 'Cyclic q-MZSV sum', Journal of Number Theory, 132 144-155 (2012) [C1]
CitationsScopus - 3Web of Science - 4
2012Warnaar SO, Zudilin V, 'Dedekind's ¿-function and Rogers-Ramanujan identities', Bulletin of the London Mathematical Society, 44 1-11 (2012) [C1]
CitationsScopus - 5Web of Science - 5
2012Chan HH, Wan G, Zudilin V, 'Complex series for 1/p', Ramanujan Journal, 29 135-144 (2012) [C1]
CitationsScopus - 1
2011Chan 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]
DOI10.1016/j.aim.2011.06.011
CitationsScopus - 11Web of Science - 10
2011Warnaar SO, Zudilin V, 'A q-rious positivity', Aequationes Mathematicae, 81 177-183 (2011) [C1]
DOI10.1007/s00010-010-0055-9
CitationsScopus - 4Web of Science - 5
2011Almkvist 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]
DOI10.1017/S0013091509000959
CitationsScopus - 8Web of Science - 9
2011Zudilin V, 'Book Review: Ramanujan's Lost Notebook. Part II, G.E. Andrews, B.C. Berndt', Journal of Approximation Theory, 163 1037-1038 (2011) [C3]
2011Gallot 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]
CitationsScopus - 3Web of Science - 4
2011Zudilin V, 'Arithmetic hypergeometric series', Russian Mathematical Surveys, 66 369-420 (2011) [C1]
DOI10.1070/RM2011v066n02ABEH004742
CitationsScopus - 8Web of Science - 4
2010Chan HH, Long L, Zudilin V, 'A supercongruence motivated by the Legendre family of elliptic curves', Mathematical Notes, 88 599-602 (2010) [C1]
DOI10.1134/S0001434610090324
CitationsScopus - 2Web of Science - 1
2010Chan HH, Zudilin V, 'New representations for apery-like sequences', Mathematika, 56 107-117 (2010) [C1]
DOI10.1112/s0025579309000436
CitationsScopus - 10Web of Science - 10
2010Fischler S, Zudilin V, 'A refinement of Nesterenko's linear independence criterion with applications to zeta values', Mathematische Annalen, 347 739-763 (2010) [C1]
DOI10.1007/s00208-009-0457-y
CitationsScopus - 5Web of Science - 5
2010Bailey DH, Borwein JM, Broadhurst D, Zudilin V, 'Experimental mathematics and mathematical physics', Contemporary Mathematics, 517 41-58 (2010) [C1]
CitationsWeb of Science - 3
Co-authorsJonathan Borwein
2010Yang Y, Zudilin V, 'On Sp4 modularity of Picard-Fuchs differential equations for Calabi-Yan threefolds', Contemporary Mathematics, 517 381-413 (2010) [C1]
DOI10.1090/conm/517
2009Zudilin V, 'Apery's theorem. Thirty years after', International Journal of Mathematics and Computer Science, 4 9-19 (2009) [C1]
2009Zudilin V, 'Ramanujan-type supercongruences', Journal of Number Theory, 129 1848-1857 (2009) [C1]
DOI10.1016/j.jnt.2009.01.01
CitationsScopus - 10Web of Science - 11
2009Krattenthaler 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]
DOI10.4064/aa136-3-4
CitationsScopus - 2Web of Science - 2
2009Zudilin V, 'A hypergeometric problem', Journal of Computational and Applied Mathematics, 233 856-857 (2009) [C1]
DOI10.1016/j.cam.2009.02.053
2008Ohno Y, Zudilin W, 'Zeta Stars', Communications in Number Theory and Physics, 2 325-347 (2008) [C1]
CitationsScopus - 20Web of Science - 16
2008Zudilin W, 'Linear independence of values of Tschakaloff functions with different parameters', Journal of Number Theory, 128 2549-2558 (2008) [C1]
DOI10.1016/j.jnt.2008.03.003
CitationsScopus - 2Web of Science - 2
2008Viola C, Zudilin W, 'Hypergeometric transformations of linear forms in one logarithm', Functiones et Approximatio Commentarii Mathematici, 39 211-222 (2008) [C1]
2007Zudilin W, 'Approximations to -, di- and tri-logarithms', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 202 450-459 (2007) [C1]
DOI10.1016/j.cam.2005.04.076Author URL
CitationsScopus - 4Web of Science - 4
2007Zudilin W, 'An elementary proof of the irrationality of Tschakaloff series', Journal of Mathematical Sciences, 146 5669-5673 (2007) [C1]
DOI10.1007/s10958-007-0382-0
2007Zudilin W, 'A new lower bound for II(3/2)kII', Journal de Theorie des Nombres de Bordeaux, 19 313-325 (2007) [C1]
2007Zudilin VV, 'Quadratic transformations and Guillera's formulas for 1/pi(2)', MATHEMATICAL NOTES, 81 297-301 (2007) [C1]
DOI10.1134/S0001434607030030Author URL
CitationsScopus - 5Web of Science - 4
2007Bundschuh P, Zudilin W, 'Irrationality measures for certain q-mathematical constants', MATHEMATICA SCANDINAVICA, 101 104-122 (2007) [C1]
Author URL
CitationsScopus - 8Web of Science - 7
2007Vaananen K, Zudilin WV, 'Linear independence of values of Tschakaloff series', RUSSIAN MATHEMATICAL SURVEYS, 62 196-198 (2007) [C1]
DOI10.1070/RM2007v062n01ABEH004386Author URL
CitationsScopus - 1
2007Zudilin VV, 'More Ramanujan-type formulae for 1/p 2', Russian Mathematical Surveys, 62 634-636 (2007) [C1]
DOI10.1070/RM2007v062n03ABEH004420
CitationsScopus - 7
2006Matala-Aho T, Vaananen K, Zudilin W, 'New irrationality measures for q-logarithms', MATHEMATICS OF COMPUTATION, 75 879-889 (2006) [C1]
Author URL
CitationsScopus - 10Web of Science - 9
2006Pilehrood KH, Pilehrood TH, Zudilin W, 'Irrationality of certain numbers that contain values of the di- and trilogarithm', MATHEMATISCHE ZEITSCHRIFT, 254 299-313 (2006) [C1]
DOI10.1007/s00209-006-0948-4Author URL
CitationsScopus - 1Web of Science - 1
2006Sondow J, Zudilin W, 'Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper', RAMANUJAN JOURNAL, 12 225-244 (2006) [C1]
DOI10.1007/s11139-006-0075-1Author URL
CitationsScopus - 8Web of Science - 9
2006Krattenthaler 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]
2006Zudilin 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=¿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.

DOI10.1007/s10958-006-0263-y
CitationsScopus - 3
2005Vaananen 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]
DOI10.4153/CMB-2005-013-5Author URL
CitationsScopus - 3Web of Science - 3
2005Zudilin W, 'Well-poised generation of Apery-like recursions', JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 178 513-521 (2005) [C1]
DOI10.1016/j.cam.2003.11.016Author URL
CitationsWeb of Science - 1
2005Zudilin WV, 'Ramanujan-type formulae and irrationality measures of some multiples of p', Sbornik Mathematics, 196 983-998 (2005)
DOI10.1070/SM2005v196n07ABEH000945
CitationsScopus - 1
2005Zudilin W, 'Computing powers of two generalizations of the logarithm', Seminaire Lotharingien de Combinatoire, 53 1-6 (2005) [C1]
2004Zudilin VV, 'Binomial sums related to rational approximations to ¿(4)', Mathematical Notes, 75 594-597 (2004)
CitationsScopus - 2
2004Zudilin VV, 'The inverse legendre transform of a certain family of sequences', Mathematical Notes, 76 276-279 (2004) [C1]
DOI10.1023/B:MATN.0000036764.72552.55
CitationsScopus - 1
2004Zudilin W, 'Binomial sums related to rational approximations to Zeta(4)', Russian Academy of Sciences: Mathematical Notes, 75 594-597 (2004) [C1]
DOI10.1023/B:MATN.0000023341.93824.fb
2004Bundschuh P, Zudilin W, 'On theorems of Gelfond and Selberg concerning integral-valued entire functions', JOURNAL OF APPROXIMATION THEORY, 130 164-178 (2004) [C1]
DOI10.1016/j.jat.2004.07.005Author URL
CitationsScopus - 5Web of Science - 5
2004Zudilin W, 'Well-poised hypergeometric transformations of Euler-type multiple integrals', JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 70 215-230 (2004) [C1]
DOI10.1112/S0024610704005472Author URL
CitationsScopus - 5Web of Science - 6
2004Zudilin W, 'Heine's basic transform and a permutation group for q-harmonic series', ACTA ARITHMETICA, 111 153-164 (2004) [C1]
DOI10.4064/aa111-2-4Author URL
CitationsScopus - 13Web of Science - 10
2004Zudilin W, 'On a combinatorial problem of Asmus Schmidt', ELECTRONIC JOURNAL OF COMBINATORICS, 11 (2004) [C1]
Author URL
CitationsWeb of Science - 5
2004Zudilin W, 'On a combinatorial problem of Asmus Schmidt', Electronic Journal of Combinatorics, 11 (2004)
CitationsScopus - 7
2004Zudilin W, 'Arithmetic of linear forms involving odd zeta values', Journal de Theorie des Nombres de Bordeaux, 16 251-291 (2004) [C1]
DOI10.5802/jtnb.447
2003Zudilin W, 'The hypergeometric equation and Ramanujan functions', RAMANUJAN JOURNAL, 7 435-447 (2003) [C1]
DOI10.1023/B:RAMA.0000012426.23921.24Author URL
CitationsScopus - 6Web of Science - 7
2003Zudilin VV, 'On the Functional Transcendence of q-Zeta Values', Mathematical Notes, 73 588-589 (2003) [C1]
DOI10.1023/A:1023275708583
CitationsScopus - 1
2003Rivoal T, Zudilin W, 'Diophantine properties of numbers related to Catalan's constant', MATHEMATISCHE ANNALEN, 326 705-721 (2003) [C1]
DOI10.1007/s00208-003-0420-2Author URL
CitationsScopus - 19Web of Science - 18
2003Zudilin VV, 'Algebraic relations for multiple zeta values', Russian Mathematical Surveys, 58 1-29 (2003) [C1]
DOI10.1070/RM2003v058n01ABEH000592
CitationsScopus - 15
2003Bertrand 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]
Author URL
CitationsWeb of Science - 4
2003Zudilin W, 'An Apery-like difference equation for Catalan's constant', ELECTRONIC JOURNAL OF COMBINATORICS, 10 (2003) [C1]
Author URL
CitationsWeb of Science - 7
2003Zudilin 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 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.

CitationsScopus - 6
2003Zudilin W, 'Well-poised hypergeometric service for diophantine problems of zeta values', Journal de Theorie des Nombres de Bordeaux, 15 593-626 (2003) [C1]
DOI10.5802/jtnb.415
2002Zudilin W, 'Remarks on irrationality of q-harmonic series', MANUSCRIPTA MATHEMATICA, 107 463-477 (2002)
DOI10.1007/s002290200249Author URL
CitationsScopus - 8Web of Science - 6
2002Zudilin VV, 'Very well-poised hypergeometric series and multiple integrals', Russian Mathematical Surveys, 57 824-826 (2002)
DOI10.1070/RM2002v057n04ABEH000542
CitationsScopus - 4
2002Zudilin WV, 'On the irrationality measure for a q-analogue of ¿(2)', Sbornik Mathematics, 193 1151-1172 (2002)
CitationsScopus - 6
2002Zudilin 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 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.

DOI10.1070/IM2002v066n03ABEH000387
CitationsScopus - 8
2002Zudilin 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) 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.

DOI10.1023/A:1015827602930
CitationsScopus - 6
2002Zudilin VV, 'A third-order Apéry-like recursion for ¿(5)', Mathematical Notes, 72 733-737 (2002)
DOI10.1023/A:1021473409544
CitationsScopus - 4
2002Zudilin VV, 'Diophantine problems for q-Zeta values', Mathematical Notes, 72 858-862 (2002)
DOI10.1023/A:1021450231834
CitationsScopus - 5
2001Zudilin VV, 'One of the eight numbers ¿(5), ¿(7),¿ , ¿(17), ¿(19) is irrational', Mathematical Notes, 70 426-431 (2001)
CitationsScopus - 1
2001Bertrand 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 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.

DOI10.1070/IM2001v065n04ABEH000345
CitationsScopus - 1
1997Zudilin VV, 'On the measure of linear and algebraic independence for values of entire hypergeometric functions', Mathematical Notes, 61 246-248 (1997)
1997Zudilin VV, 'Recurrent sequences and the measure of irrationality of values of elliptic integrals', Mathematical Notes, 61 657-661 (1997)
1996Zudilin VV, 'On the algebraic structure of functional matrices of special form', Mathematical Notes, 60 642-648 (1996)
Show 77 more journal articles

Conference (5 outputs)

YearCitationAltmetricsLink
2008Almkvist 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]
2008Zudilin W, 'Ramanujan-type formulae for 1/p: A second wind?', Modular Forms and String Duality - Fields Institute Communications, Banff, Canada (2008) [E1]
CitationsWeb of Science - 20
2008Bundschuh P, Zudilin W, 'Rational approximations to a q-analogue of p and some other q-series', Diophantine Approximation, Vienna, Austria (2008) [E1]
CitationsScopus - 1
2007Zudilin WV, 'More Ramanujan-type formulae for 1/pi(2)', RUSSIAN MATHEMATICAL SURVEYS, Steklov Math Inst, Moscow, RUSSIA (2007)
DOI10.1070/RM2007v062n03ABEH004420.Author URL
CitationsWeb of Science - 10
2006Almkvist G, Zudilin W, 'Differential equations, mirror maps and zeta values', Mirror Symmetry V, Banff, Canada (2006) [E1]
Show 2 more conferences
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Grants and Funding

Summary

Number of grants2
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 bodyARC (Australian Research Council)
Project TeamProfessor Ole Warnaar, Professor Wadim Zudilin
SchemeDiscovery Projects
RoleLead
Funding Start2014
Funding Finish2014
GNoG1301362
Type Of FundingAust Competitive - Commonwealth
Category1CS
UONY

20111 grants / $255,000

Arithmetic hypergeometric series$255,000

Funding body: ARC (Australian Research Council)

Funding bodyARC (Australian Research Council)
Project TeamProfessor Wadim Zudilin
SchemeDiscovery Projects
RoleLead
Funding Start2011
Funding Finish2011
GNoG1000167
Type Of FundingAust Competitive - Commonwealth
Category1CS
UONY
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Research Supervision

Past Supervision

YearResearch Title / Program / Supervisor Type
2015Arithmetic Applications of Hankel Determinants
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
2013Random Walks, Elliptic Integrals and Related Constants
Mathematics, Faculty of Science and Information Technology
Co-Supervisor
2011'Arithmetic applications of the theory of hypergeometric series'
Math Sc Not Elsewhere Classifi, Unknown
Principal Supervisor
2011'Arithmetic properties of the values of certain analytical functions'
Math Sc Not Elsewhere Classifi, Unknown
Principal Supervisor
2007Ramanujan'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

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

Office

Room236
BuildingV
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