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For publications that are currently unpublished or inpress, details are shown in italics.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 (28 outputs)
Year  Citation  Altmetrics  Link  

2016  Coons Jr MJ, Catt E, Velich J, 'Strong normality and generalised CopelandErdos numbers', Integers, 16 110 (2016)  
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]


Show 25 more journal articles 
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 