Dr Michael Coons Jr
ARC DECRA Fellow
School of Mathematical and Physical Sciences
 Email:michael.coons@newcastle.edu.au
 Phone:(02) 4921 5364
Career Summary
Biography
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 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Journal article (25 outputs)
Year  Citation  Altmetrics  Link  

2016 
Brent RP, Coons M, Zudilin W, 'Algebraic Independence of Mahler Functions via Radial Asymptotics', International Mathematics Research Notices, 2016 571603 (2016) [C1] Â© 2015 The Author(s). Published by Oxford University Press. All rights reserved. We present a new method for algebraic independence results in the context of Mahler's method. In ... [more] Â© 2015 The Author(s). Published by Oxford University Press. All rights reserved. We present a new method for algebraic independence results in the context of Mahler's method. In particular, our method uses the asymptotic behavior of a Mahler function f (z) as z goes radially to a root of unity to deduce algebraic independence results about the values of f (z) at algebraic numbers. We apply our method to the canonical example of a degree two Mahler function; that is, we apply it to F (z), the power series solution to the functional equation F (z)  (1 + z+ z2)F (z4) + z4F (z16)=0. Specifically, we prove that the functions F(z), F (z4), F' (z), and F'(z4) are algebraically independent over C(z). An application of a celebrated result of Ku. Nishioka then allows one to replace C(z) by Q when evaluating these functions at a nonzero algebraic number a in the unit disc.


2016 
Bell JP, Coons M, Hare KG, 'Growth degree classification for finitely generated semigroups of integer matrices', Semigroup Forum, 92 2344 (2016)


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 co... [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, 'Regular sequences and the joint spectral radius.', CoRR, abs/1511.07535 (2015)  
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</su... [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 22 more journal articles 
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  2016 
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  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 

2015  PhD 
Functional Analysis and its Applications PhD (Mathematics), Faculty of Science and Information Technology, The University of Newcastle CoSupervisor 
Past Supervision
Year  Level of Study  Research Title / Program / Supervisor Type 

2015  PhD 
Arithmetic Applications of Hankel Determinants PhD (Mathematics), Faculty of Science and Information Technology, The University of Newcastle Principal Supervisor 
Dr Michael Coons Jr
Position
ARC DECRA Fellow
CARMA
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology
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 