Dr Michael Coons Jr
Senior Lecturer
School of Mathematical and Physical Sciences
 Email:michael.coons@newcastle.edu.au
 Phone:(02) 4921 5364
Career Summary
Biography
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 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Journal article (34 outputs)
Year  Citation  Altmetrics  Link  

2017 
COONS M, TACHIYA Y, 'TRANSCENDENCE OVER MEROMORPHIC FUNCTIONS', Bulletin of the Australian Mathematical Society, 17 (2017) Â© 2017 Australian Mathematical Publishing Association Inc.In this short note, considering functions, we show that taking an asymptotic viewpoint allows one to prove strong transc... [more] Â© 2017 Australian Mathematical Publishing Association Inc.In this short note, considering functions, we show that taking an asymptotic viewpoint allows one to prove strong transcendence statements in many general situations. In particular, as a consequence of a more general result, we show that if (Formula presented.) is a power series with coefficients from a finite set, then (Formula presented.) is either rational or it is transcendental over the field of meromorphic functions.


2017  Coons Jr MJ, Spiegelhofer L, 'The maximal order of hyper(bary)expansions', The Electronic Journal of Combinatorics, 24 18 (2017)  
2017 
Bell JP, Coons M, 'Transcendence tests for mahler functions', Proceedings of the American Mathematical Society, 145 10611070 (2017) Â© 2016 American Mathematical Society.We give two tests for transcendence of Mahler functions. For our first, we introduce the notion of the eigenvalue Â¿F of a Mahler function F ... [more] Â© 2016 American Mathematical Society.We give two tests for transcendence of Mahler functions. For our first, we introduce the notion of the eigenvalue Â¿F of a Mahler function F (z) and develop a quick test for the transcendence of F (z) over A(z), which is determined by the value of the eigenvalue Â¿F. While our first test is quick and applicable for a large class of functions, our second test, while a bit slower than our first, is universal; it depends on the rank of a certain Hankel matrix determined by the initial coefficients of F (z). We note that these are the first transcendence tests for Mahler functions of arbitrary degree. Several examples and applications are given.


2016  Catt E, Coons Jr MJ, Velich J, 'Strong normality and generalised CopelandErdos numbers', Integers, 16 110 (2016) [C1]  
2016  Coons Jr MJ, 'Zero order estimates for Mahler functions', New Zealand Journal of Mathematics, 46 8388 (2016) [C1]  
2016 
Brent RP, Coons JR M, Zudilin V, 'Algebraic Independence of Mahler Functions via Radial Asymptotics', International Mathematics Research Notices, 2016 571603 (2016) [C1]


2016 
Coons M, Hussain M, Wang BW, 'A DICHOTOMY LAW FOR THE DIOPHANTINE PROPERTIES IN betaDYNAMICAL SYSTEMS', MATHEMATIKA, 62 884897 (2016) [C1]


2016 
Bell JP, Coons M, Hare KG, 'Growth degree classification for finitely generated semigroups of integer matrices', Semigroup Forum, 92 2344 (2016) [C1] Â© 2015, Springer Science+Business Media New York.Let A be a finite set of dÃd matrices with integer entries and let (Formula presented.) be the maximum norm of a product of n el... [more] Â© 2015, Springer Science+Business Media New York.Let A be a finite set of dÃd matrices with integer entries and let (Formula presented.) be the maximum norm of a product of n elements of A. In this paper, we classify gaps in the growth of Pn; specifically, we prove that (Formula presented.). This has applications to the growth of regular sequences as defined by Allouche and Shallit.


2015 
Borwein JM, Bugeaud Y, Coons M, 'The Legacy of Kurt Mahler', Notices of the American Mathematical Society, 62 526531 (2015) [C3]


2015 
Bell JP, Bugeaud Y, Coons M, 'Diophantine approximation of Mahler numbers', Proceedings of the London Mathematical Society, 110 11571206 (2015) [C1] Â© 2015 London Mathematical Society.Suppose that F(x) Â¿ Z[x] is a Mahler function and that 1/b is in the radius of convergence of F(x) for an integer b = 2. In this paper, we con... [more] Â© 2015 London Mathematical Society.Suppose that F(x) Â¿ Z[x] is a Mahler function and that 1/b is in the radius of convergence of F(x) for an integer b = 2. In this paper, we consider the approximation of F(1/b) by algebraic numbers. In particular, we prove that F(1/b) cannot be a Liouville number. If, in addition, F(x) is regular, we show that F(1/b) is either rational or transcendental, and in the latter case that F(1/b) is an Snumber or a Tnumber in Mahler's classification of real numbers.


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 109111 (2015) [C3]


2015 
Coons M, Winning H, 'Powers of two modulo powers of three', Journal of Integer Sequences, 18 (2015) [C1] Â© 2015 University of Waterloo. All rights reserved.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... [more] Â© 2015 University of Waterloo. All rights reserved.Since 2 is a primitive root of 3^{m} for each positive integer m, the set of points {(n, 2^{n} mod 3^{m}): n = 0}, viewed as a subset of Z 

2014  Coons M, Tyler J, 'The maximal order of SternÂ¿s diatomic sequence', Moscow Journal of Combinatorics and Number Theory, 4 313 (2014) [C1]  
2014 
Bell JP, Coons M, Hare KG, 'The minimal growth of a kregular sequence', Bulletin of the Australian Mathematical Society, 90 195203 (2014) [C1]


2014 
Coons M, 'AN ARITHMETICAL EXCURSION VIA STONEHAM NUMBERS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 96 303315 (2014) [C1]


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 3965 (2013) [C1]


2013 
Bell JP, Coons M, Rowland E, 'The rationaltranscendental dichotomy of Mahler functions', Journal of Integer Sequences, 16 Article 13.2.1011 (2013) [C1]


2010 
Coons M, '(Non) automaticity of number theoretic functions', Journal de Theorie des Nombres de Bordeaux, 22 339352 (2010) [C1] Â© UniversitÃ© Bordeaux 1, 2010, tous droits rÃ©servÃ©s.Denote by Â¿(n) LiouvilleÂ¿s function concerning the parity of the number of prime divisors of n. Using a theorem of Allouc... [more] Â© UniversitÃ© Bordeaux 1, 2010, tous droits rÃ©servÃ©s.Denote by Â¿(n) LiouvilleÂ¿s function concerning the parity of the number of prime divisors of n. Using a theorem of Allouche, MendÃ¨s France, and PeyriÃ¨re and many classical results from the theory of the distribution of prime numbers, we prove that Â¿(n) is not Â¿automatic for any k > 2. This yields that S 8n=1 Â¿(n) Xn e Fp[[X]] is transcendental over Fp(X) for any prime p > 2. Similar results are proven (or reproven) for many common numbertheoretic functions, including f, Âµ, O, Â¿, Â¿, and others.


Show 31 more journal articles 
Grants and Funding
Summary
Number of grants  5 

Total funding  $434,994 
Click on a grant title below to expand the full details for that specific grant.
20142 grants / $421,230
Diophantine approximation, transcendence, and related structures$404,338
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  2016 
GNo  G1300416 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
DVC(R) Research Support for DECRA (DE14) $16,892
Funding body: University of Newcastle
Funding body  University of Newcastle 

Project Team  Doctor Michael Coons Jr 
Scheme  DECRA Support 
Role  Lead 
Funding Start  2014 
Funding Finish  2016 
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 
Research Supervision
Number of supervisions
Total current UON EFTSL
Current Supervision
Commenced  Level of Study  Research Title  Program  Supervisor Type 

2014  PhD  Parallelisation, Precision, and Reproducibility in Pure Mathematical Computation  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
Past Supervision
Year  Level of Study  Research Title  Program  Supervisor Type 

2015  PhD  Arithmetic Applications of Hankel Determinants  PhD (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
Dr Michael Coons Jr
Position
Senior Lecturer
CARMA
School of Mathematical and Physical Sciences
Faculty of Science
Contact Details
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 