Dr Michael Coons Jr

ARC DECRA Fellow

School of Mathematical and Physical Sciences

Career Summary

Biography

Research Expertise
Number Theory

Teaching Expertise
Pure Mathematics

Qualifications

  • PhD (Mathematics), Simon Fraser University

Keywords

  • Number Theory
  • Pure Mathematics

Fields of Research

Code Description Percentage
010101 Algebra and Number Theory 100

Professional Experience

UON Appointment

Title Organisation / Department
Senior Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Journal article (24 outputs)

Year Citation Altmetrics Link
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 Wadim Zudilin
2015 Coons M, 'On the rational approximation of the sum of the reciprocals of the Fermat numbers (vol 30, pg 39, 2013)', RAMANUJAN JOURNAL, 37 109-111 (2015)
DOI 10.1007/s11139-015-9685-9
2015 Bell JP, Coons M, Hare KG, 'Growth degree classification for finitely generated semigroups of integer matrices', Semigroup Forum, (2015)

Let (Formula presented.) be a finite set of (Formula presented.) matrices with integer entries and let (Formula presented.) be the maximum norm of a product of (Formula presented.... [more]

Let (Formula presented.) be a finite set of (Formula presented.) matrices with integer entries and let (Formula presented.) be the maximum norm of a product of (Formula presented.) elements of (Formula presented.). In this paper, we classify gaps in the growth of (Formula presented.); specifically, we prove that (Formula presented.) This has applications to the growth of regular sequences as defined by Allouche and Shallit.

DOI 10.1007/s00233-015-9725-1
2015 Bell JP, Bugeaud Y, Coons M, 'Diophantine approximation of Mahler numbers', PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 110 1157-1206 (2015)
DOI 10.1112/plms/pdv016
2015 Coons M, Winning H, 'Powers of two modulo powers of three', Journal of Integer Sequences, 18 (2015)

Since 2 is a primitive root of 3<sup>m</sup> for each positive integer m, the set of points {(n, 2<sup>n</sup> mod 3<sup>m</sup>): n = 0}, viewed as a subset of Z<inf>=</inf><inf>... [more]

Since 2 is a primitive root of 3m for each positive integer m, the set of points {(n, 2n mod 3m): n = 0}, viewed as a subset of Z=0 ×Z=0 is bi-periodic, with minimal periods f(3m) (horizontally) and 3m (vertically). We show that if one considers the classes of n modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of Stoneham numbers.

2014 Coons M, Tyler J, 'The maximal order of Stern¿s diatomic sequence', Moscow Journal of Combinatorics and Number Theory, 4 3-13 (2014) [C1]
2014 Bell JP, Coons M, Hare KG, 'The minimal growth of a k-regular sequence', Bulletin of the Australian Mathematical Society, 90 195-203 (2014) [C1]
DOI 10.1017/S0004972714000197
Citations Scopus - 1Web of Science - 1
2014 Coons M, 'AN ARITHMETICAL EXCURSION VIA STONEHAM NUMBERS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 96 303-315 (2014) [C1]
DOI 10.1017/S1446788713000682
Citations Scopus - 1
2013 Coons M, 'Transcendental solutions of a class of minimal functional equations', Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, 56 283-291 (2013) [C1]
DOI 10.4153/CMB-2011-157-x
2013 Coons M, 'On the rational approximation of the sum of the reciprocals of the Fermat numbers', Ramanujan Journal. An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan, 30 39-65 (2013) [C1]
DOI 10.1007/s11139-012-9410-x
Citations Scopus - 6Web of Science - 7
2013 Bell JP, Coons M, Rowland E, 'The rational-transcendental dichotomy of Mahler functions', Journal of Integer Sequences, 16 Article 13.2.10-11 (2013) [C1]
Citations Scopus - 1
2012 Bell JP, Bruin N, Coons M, 'Transcendence of generating functions whose coefficients are multiplicative', Transactions of the American Mathematical Society, 364 933-959 (2012) [C1]
DOI 10.1090/S0002-9947-2011-05479-6
Citations Scopus - 1
2012 Coons M, 'Extension of some theorems of W. Schwarz', Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, 55 60-66 (2012) [C1]
DOI 10.4153/CMB-2011-037-9
Citations Scopus - 3Web of Science - 3
2012 Coons M, 'A note on two conjectures associated to Goldbach's problem', Publicationes Mathematicae Debrecen, 80 343-345 (2012) [C1]
DOI 10.5486/PMD.2012.5037
2012 Coons M, Vrbik P, 'An irrationality measure for regular paperfolding numbers', Journal of Integer Sequences, 15 (2012) [C1]
2012 Coons M, 'A correlation identity for Stern's sequence', Integers, 12 459-464 (2012) [C1]
DOI 10.1515/integers-2011-0116
2011 Coons M, 'On some conjectures concerning Stern's sequence and its twist', Integers, 11 775-789 (2011) [C1]
DOI 10.1515/INTEG.2011.003
2011 Coons M, Shallit J, 'A pattern sequence approach to Stern's sequence', Discrete Mathematics, 311 2630-2633 (2011) [C1]
DOI 10.1016/j.disc.2011.07.029
Citations Web of Science - 1
2011 Coons M, Dahmen SR, 'On the residue class distribution of the number of prime divisors of an integer', Nagoya Mathematical Journal, 202 15-22 (2011) [C1]
Citations Scopus - 1Web of Science - 1
2010 Coons M, 'The transcendence of series related to Stern's diatomic sequence', International Journal of Number Theory, 6 211-217 (2010) [C1]
DOI 10.1142/S1793042110002958
Citations Scopus - 8Web of Science - 7
2010 Borwein P, Choi SKK, Coons M, 'Completely multiplicative functions taking values in $-1,1$', Transactions of the American Mathematical Society, 362 6279-6291 (2010) [C1]
DOI 10.1090/S0002-9947-2010-05235-3
Citations Scopus - 5Web of Science - 5
2010 Coons M, '(Non)automaticity of number theoretic functions', Journal de Théorie des Nombres de Bordeaux, 22 339-352 (2010) [C1]
2009 Borwein P, Coons M, 'Transcendence of power series for some number theoretic functions', Proceedings of the American Mathematical Society, 137 1303-1305 (2009) [C1]
DOI 10.1090/S0002-9939-08-09737-2
Citations Scopus - 5Web of Science - 4
2009 Coons M, Kirsten K, 'General moment theorems for nondistinct unrestricted partitions', Journal of Mathematical Physics, 50 013517-19 (2009) [C1]
DOI 10.1063/1.3050060
Show 21 more journal articles
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Grants and Funding

Summary

Number of grants 5
Total funding $414,499

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


20142 grants / $400,735

Diophantine approximation, transcendence, and related structures$385,735

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Doctor Michael Coons Jr
Scheme Discovery Early Career Researcher Award (DECRA)
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1300416
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

DVC(R) Research Support for DECRA (DE14) $15,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Michael Coons Jr
Scheme Special Project Grant
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1400115
Type Of Funding Internal
Category INTE
UON Y

20132 grants / $8,764

Faculty Visiting Fellowship 2013$6,764

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team Doctor Michael Coons Jr
Scheme Visiting Fellowship
Role Lead
Funding Start 2013
Funding Finish 2013
GNo G1401133
Type Of Funding Internal
Category INTE
UON Y

Faculty ECA Networking/Conference Grant 2013$2,000

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team Doctor Michael Coons Jr
Scheme Early Career Academic (ECA) Networking/Conference Grant
Role Lead
Funding Start 2013
Funding Finish 2014
GNo G1401109
Type Of Funding Internal
Category INTE
UON Y

20121 grants / $5,000

Complexity and approximation in the context of Mahler's method$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Michael Coons Jr
Scheme New Staff Grant
Role Lead
Funding Start 2012
Funding Finish 2012
GNo G1201156
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed1
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
Principal Supervisor
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Dr Michael Coons Jr

Position

ARC DECRA Fellow
CARMA
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Contact Details

Email michael.coons@newcastle.edu.au
Phone (02) 4921 5364
Mobile None
Fax (02) 4921 6898

Office

Room V231
Building Mathematics Building
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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