Associate Professor Michael Coons Jr
Associate Professor
School of Information and Physical Sciences (Mathematics)
 Email:michael.coons@newcastle.edu.au
 Phone:(02) 4921 5364
Career Summary
Biography
A/Prof Coons is a mathematician with a passion for excellence and discovery. He has been a Fulbright Scholar (Hungary), a FieldsOntario Fellow (Canada) and a DECRA Fellow of the Australian Research Council, and is Deputy EditorinChief of the Journal of the Australian Mathematical Society.
While A/Prof Coons’ early work was in number theory, he is now a pure mathematician in a broad sense. The problems he works on are multifaceted and lend well to collaboration across areas of pure and applied mathematics. At heart, he is a problem solver, often developing mathematical relationships at the boundaries of algebra, analysis, computer science, fractal geometry, number theory and dynamics.
A/Prof Coons’ research is pursued with international colleagues, disseminated internationally and attracts international attention. He has written papers with 31 different coauthors including 20 international coauthors based in 9 different countries outside Australia. A/Prof Coons has presented his research in several countries, having given over 100 research talks, with over 70 invited. He is regularly invited to give research presentations and collaborate at other universities and research institutes as well as at prestigious conferences and workshops. The visibility of his research and reputation has been highlighted by invited participation to several of the world's most prestigious mathematical research venues including:
 Banff International Research Station (BIRS), Banff, Canada,
 Centre International de Rencontres Mathématiques (CIRM), Luminy, France,
 Erwin Schödinger International Institute for Mathematics and Physics (ESI), Vienna, Austria,
 French National Institute for computer science and applied math. (INRIA), Saclay, France,
 Hungarian Academy of Sciences (Rényi Institute), Budapest, Hungary,
 Institut Henri Poincaré, Paris, France,
 Mathematisches Forschungsinstitut Oberwolfach (MFO), Oberwolfach, Germany.
A/Prof Coons has taught mathematics in the United States, Canada, and Australia. His teaching experience ranges from firstyear undergraduate courses to highlevel specialised undergraduate, honours, and postgraduate courses. In every course he teaches, he strives for personal excellence and consistently motivates students to achieve strong outcomes.
A/Prof Coons is dedicated to the service of the academic and university communities at all levels. Here at Newcastle, he has served on academic governance boards at the Faculty and University levels, as well as the Executive Committee of CARMA, including a stint as its Deputy Director. In 2014, he represented the Australian Academy of Sciences as one of four Delegates to the General Assembly of the International Mathematical Union (ICM Korea). Additionally, he was Early Career Representative of the Australian Mathematical Society (20142018).
See https://mcoonsmath.github.io for uptodate and more detailed information.
Qualifications
 PhD (Mathematics), Simon Fraser University
Keywords
 Aperiodic Order
 Dynamical Systems
 Fractal Geometry
 Mathematical Physics
 Number Theory
 Pure Mathematics
 Theoretical Computer Science
Fields of Research
Code  Description  Percentage 

490105  Dynamical systems in applications  10 
490401  Algebra and number theory  50 
490409  Ordinary differential equations, difference equations and dynamical systems  40 
Professional Experience
UON Appointment
Title  Organisation / Department 

Associate Professor  University of Newcastle School of Mathematical and Physical Sciences Australia 
Awards
Prize
Year  Award 

2017 
MahonyNeumannRoom Prize Australian Mathematical Society 
Research Award
Year  Award 

2014 
Distinguished Early Career Research Award ARC (Australian Research Council) 
Scholarship
Year  Award 

2005 
Fulbright Scholar United States of America, Department of State 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Book (1 outputs)
Year  Citation  Altmetrics  Link 

2019  Mahler Selecta, Documenta Math., Deutsche MathematikerVereinigung, Berlin (2019) 
Chapter (3 outputs)
Year  Citation  Altmetrics  Link  

2019  Baake M, Borwein J, Bugeaud Y, Coons Jr M, 'Introduction', Mahler Selecta, Documenta Math., Deutsche MathematikerVereinigung, Berlin 311 (2019)  
2019  Baake M, Borwein J, Bugeaud Y, Coons Jr M, 'Introduction', Mahler Selecta, Documenta Math., Deutsche MathematikerVereinigung, Berlin 311 (2019)  
2018 
Coons Jr MJ, Spiegelhofer L, 'Number Theoretic Aspects of Regular Sequences', Sequences, Groups, and Number Theory, Birkhäuser, Cham, Switzerland 3787 (2018) [B1]

Journal article (51 outputs)
Year  Citation  Altmetrics  Link  

2021 
Baake M, Coons M, Evans J, Gohlke P, 'On a family of singular continuous measures related to the doubling map', Indagationes Mathematicae, 32 847860 (2021) Here, we study some measures that can be represented by infinite Riesz products of 1periodic functions and are related to the doubling map. We show that these measures are purely... [more] Here, we study some measures that can be represented by infinite Riesz products of 1periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy superpolynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue¿Morse measure.


2021 
Coons M, Evans J, 'A sequential view of selfsimilar measures; or, what the ghosts of Mahler and cantor can teach us about dimension', Journal of Integer Sequences, 24 110 (2021) [C1] We show that a missing qary digit set F ¿ [0, 1] has a corresponding naturally associated countable binary qautomatic sequence f. Using this correspondence, we show that the Hau... [more] We show that a missing qary digit set F ¿ [0, 1] has a corresponding naturally associated countable binary qautomatic sequence f. Using this correspondence, we show that the Hausdorff dimension of F is equal to the baseq logarithm of the Mahler eigenvalue of f. In addition, we demonstrate that the standard mass distribution ¿F supported on F is equal to the ghost measure µf of f. 

2021 
Baake M, Coons M, 'Scaling of the diffraction measure of kfree integers near the origin', Michigan Mathematical Journal, 70 213221 (2021) [C1] We derive asymptotics for the scaling of the total diffraction intensity for the set of kfree integers near the origin, which is a measure for the degree of patch fluctuations.... [more] We derive asymptotics for the scaling of the total diffraction intensity for the set of kfree integers near the origin, which is a measure for the degree of patch fluctuations.


2020 
Coons M, 'DEGREEONE MAHLER FUNCTIONS: ASYMPTOTICS, APPLICATIONS and SPECULATIONS', Bulletin of the Australian Mathematical Society, 102 399409 (2020) [C1] We present a complete characterisation of the radial asymptotics of degreeone Mahler functions as approaches roots of unity of degree, where is the base of the Mahler function, a... [more] We present a complete characterisation of the radial asymptotics of degreeone Mahler functions as approaches roots of unity of degree, where is the base of the Mahler function, as well as some applications concerning transcendence and algebraic independence. For example, we show that the generating function of the ThueMorse sequence and any Mahler function (to the same base) which has a nonzero Mahler eigenvalue are algebraically independent over. Finally, we discuss asymptotic bounds towards generic points on the unit circle.


2019 
Bell JP, Chyzak F, Coons M, Dumas P, 'BECKER'S CONJECTURE ON MAHLER FUNCTIONS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372 34053423 (2019)


2019  Bugeaud Y, Coons Jr M, 'A Mahler Miscellany', Documenta Mathematica. Journal of the German Association of Mathematicians, Extra Vol. 179190 (2019) [C1]  
2018 
Coons Jr MJ, 'Proof of Northshield s conjecture concerning an analogue of Stern s sequence for Z[v2]', Australasian Journal of Combinatorics, 71 113120 (2018) [C1]


2018  Coons Jr MJ, 'Mahler takes a regular view of Zaremba', Integers : Electronic Journal of Combinatorial Number Theory, 18A 115 (2018) [C1]  
2018 
Baake M, Coons Jr MJ, 'A natural probability measure derived from Stern's diatomic sequence', ACTA ARITHMETICA, 183 8799 (2018) [C1]


2017 
Coons Jr MJ, Spiegelhofer L, 'The maximal order of hyper(bary)expansions', The Electronic Journal of Combinatorics, 24 18 (2017) [C1]


2017 
Coons M, Tachiya Y, 'TRANSCENDENCE OVER MEROMORPHIC FUNCTIONS', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 95 393399 (2017) [C1]


2017 
Coons M, 'Regular Sequences and the Joint Spectral Radius', INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE, 28 135140 (2017) [C1]


2017 
Coons Jr MJ, 'Extension of a theorem of Duffin and Schaeffer', Journal of Integer Sequences, 20 14 (2017) [C1]


2017  Coons Jr MJ, 'An asymptotic approach in Mahler's method', New Zealand Journal of Mathematics, 47 2742 (2017) [C1]  
2017 
Bell JP, Coons M, 'TRANSCENDENCE TESTS FOR MAHLER FUNCTIONS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145 10611070 (2017) [C1]


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] Let A be a finite set of d×d 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... [more] Let A be a finite set of d×d 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] Suppose that F(x) ¿ 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 ... [more] Suppose that F(x) ¿ 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] 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}, view... [more] 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>0</inf> ×Z<inf>=</inf><inf>0</inf> is biperiodic, with minimal periods f(3<sup>m</sup>) (horizontally) and 3<sup>m</sup> (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, 4 313 (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 (2013) [C1]


2010 
Coons M, '(Non) automaticity of number theoretic functions', Journal de Theorie des Nombres de Bordeaux, 22 339352 (2010) [C1] Denote by ¿(n) Liouville¿s function concerning the parity of the number of prime divisors of n. Using a theorem of Allouche, Mendès France, and Peyrière and many classical results... [more] Denote by ¿(n) Liouville¿s function concerning the parity of the number of prime divisors of n. Using a theorem of Allouche, Mendès France, and Peyrière and many classical results from the theory of the distribution of prime numbers, we prove that ¿(n) is not ¿automatic for any k > 2. This yields that S 8n=1 ¿(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, µ, O, ¿, ¿, and others.


Show 48 more journal articles 
Conference (1 outputs)
Year  Citation  Altmetrics  Link  

2020 
Baake M, Coons Jr M, Manibo N, 'Binary ConstantLength Substitutions and Mahler Measures of Borwein Polynomials', Springer Proceedings in Mathematics and Statistics, Newcastle, Australia (2020) [E1]

Research Collaborations
The map is a representation of a researchers coauthorship with collaborators across the globe. The map displays the number of publications against a country, where there is at least one coauthor based in that country. Data is sourced from the University of Newcastle research publication management system (NURO) and may not fully represent the authors complete body of work.
Country  Count of Publications  

Australia  26  
Canada  18  
Germany  5  
France  5  
Austria  2  
More... 
Associate Professor Michael Coons Jr
Position
Associate Professor
CARMA
School of Information and Physical Sciences
College of Engineering, Science and Environment
Focus area
Mathematics
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 