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

CodeDescriptionPercentage
010101Algebra and Number Theory100

Professional Experience

UON Appointment

DatesTitleOrganisation / Department
1/01/2015 - Senior LecturerUniversity 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For publications that are currently unpublished or in-press, details are shown in italics.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 (23 outputs)

YearCitationAltmetricsLink
2015Coons 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)
DOI10.1007/s11139-015-9685-9Author URL
2015Bell 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.) 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.

DOI10.1007/s00233-015-9725-1
2015Bell JP, Bugeaud Y, Coons M, 'Diophantine approximation of Mahler numbers', PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 110 1157-1206 (2015)
DOI10.1112/plms/pdv016Author URL
2015Coons M, Winning H, 'Powers of two modulo powers of three', Journal of Integer Sequences, 18 (2015)

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.

2014Coons M, Tyler J, 'The maximal order of Stern¿s diatomic sequence', Moscow Journal of Combinatorics and Number Theory, 4 3-13 (2014) [C1]
2014Bell JP, Coons M, Hare KG, 'The minimal growth of a k-regular sequence', Bulletin of the Australian Mathematical Society, 90 195-203 (2014) [C1]
DOI10.1017/S0004972714000197
CitationsScopus - 1
2014Coons M, 'AN ARITHMETICAL EXCURSION VIA STONEHAM NUMBERS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 96 303-315 (2014) [C1]
DOI10.1017/S1446788713000682Author URL
CitationsScopus - 1
2013Coons M, 'Transcendental solutions of a class of minimal functional equations', Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, 56 283-291 (2013) [C1]
DOI10.4153/CMB-2011-157-x
2013Coons 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]
DOI10.1007/s11139-012-9410-x
CitationsScopus - 5Web of Science - 7
2013Bell JP, Coons M, Rowland E, 'The rational-transcendental dichotomy of Mahler functions', Journal of Integer Sequences, 16 Article 13.2.10-11 (2013) [C1]
Author URL
2012Bell JP, Bruin N, Coons M, 'Transcendence of generating functions whose coefficients are multiplicative', Transactions of the American Mathematical Society, 364 933-959 (2012) [C1]
DOI10.1090/S0002-9947-2011-05479-6
CitationsScopus - 1
2012Coons M, 'Extension of some theorems of W. Schwarz', Canadian Mathematical Bulletin. Bulletin Canadien de Mathématiques, 55 60-66 (2012) [C1]
DOI10.4153/CMB-2011-037-9
CitationsScopus - 3Web of Science - 3
2012Coons M, 'A note on two conjectures associated to Goldbach's problem', Publicationes Mathematicae Debrecen, 80 343-345 (2012) [C1]
DOI10.5486/PMD.2012.5037
2012Coons M, Vrbik P, 'An irrationality measure for regular paperfolding numbers', Journal of Integer Sequences, 15 (2012) [C1]
2012Coons M, 'A correlation identity for Stern's sequence', Integers, 12 459-464 (2012) [C1]
DOI10.1515/integers-2011-0116
2011Coons M, 'On some conjectures concerning Stern's sequence and its twist', Integers, 11 775-789 (2011) [C1]
DOI10.1515/INTEG.2011.003
2011Coons M, Shallit J, 'A pattern sequence approach to Stern's sequence', Discrete Mathematics, 311 2630-2633 (2011) [C1]
DOI10.1016/j.disc.2011.07.029
CitationsWeb of Science - 1
2011Coons 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]
CitationsScopus - 1Web of Science - 1
2010Coons M, 'The transcendence of series related to Stern's diatomic sequence', International Journal of Number Theory, 6 211-217 (2010) [C1]
DOI10.1142/S1793042110002958
CitationsScopus - 7Web of Science - 6
2010Borwein P, Choi SKK, Coons M, 'Completely multiplicative functions taking values in $-1,1$', Transactions of the American Mathematical Society, 362 6279-6291 (2010) [C1]
DOI10.1090/S0002-9947-2010-05235-3
CitationsScopus - 4Web of Science - 5
2010Coons M, '(Non)automaticity of number theoretic functions', Journal de Théorie des Nombres de Bordeaux, 22 339-352 (2010) [C1]
2009Borwein P, Coons M, 'Transcendence of power series for some number theoretic functions', Proceedings of the American Mathematical Society, 137 1303-1305 (2009) [C1]
DOI10.1090/S0002-9939-08-09737-2
CitationsScopus - 5Web of Science - 4
2009Coons M, Kirsten K, 'General moment theorems for nondistinct unrestricted partitions', Journal of Mathematical Physics, 50 013517-19 (2009) [C1]
DOI10.1063/1.3050060
Show 20 more journal articles
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Grants and Funding

Summary

Number of grants5
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 bodyARC (Australian Research Council)
Project TeamDoctor Michael Coons Jr
SchemeDiscovery Early Career Researcher Award (DECRA)
RoleLead
Funding Start2014
Funding Finish2014
GNoG1300416
Type Of FundingAust Competitive - Commonwealth
Category1CS
UONY

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

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Michael Coons Jr
SchemeSpecial Project Grant
RoleLead
Funding Start2014
Funding Finish2014
GNoG1400115
Type Of FundingInternal
CategoryINTE
UONY

20132 grants / $8,764

Faculty Visiting Fellowship 2013$6,764

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

Funding bodyUniversity of Newcastle - Faculty of Science & IT
Project TeamDoctor Michael Coons Jr
SchemeVisiting Fellowship
RoleLead
Funding Start2013
Funding Finish2013
GNoG1401133
Type Of FundingInternal
CategoryINTE
UONY

Faculty ECA Networking/Conference Grant 2013$2,000

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

Funding bodyUniversity of Newcastle - Faculty of Science & IT
Project TeamDoctor Michael Coons Jr
SchemeEarly Career Academic (ECA) Networking/Conference Grant
RoleLead
Funding Start2013
Funding Finish2014
GNoG1401109
Type Of FundingInternal
CategoryINTE
UONY

20121 grants / $5,000

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

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Michael Coons Jr
SchemeNew Staff Grant
RoleLead
Funding Start2012
Funding Finish2012
GNoG1201156
Type Of FundingInternal
CategoryINTE
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
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

Emailmichael.coons@newcastle.edu.au
Phone(02) 4921 5364
MobileNone
Fax(02) 4921 6898

Office

RoomV231
BuildingMathematics Building
LocationCallaghan
University Drive
Callaghan, NSW 2308
Australia
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