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


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.



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] 


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 e... [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 P n ; 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 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, 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 < su... [more]
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 > ): n = 0}, viewed as a subset of Z < inf > = < /inf > < inf > 0 < /inf > ÃZ < 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 SternÂ¿s diatomic sequence', Moscow Journal of Combinatorics and Number Theory, 4 313 (2014) [C1] 


2014 
Borwein JM, Bugeaud Y, Coons Jr MJ, 'The legacy of Kurt Mahler', Gazette of the Australian Mathematical Society, 41 1121 (2014) [O1] 


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 Jr MJ, Borwein JM, Bugeaud Y, 'The legacy of Kurt Mahler', Newsletter of the European Mathematical Society, 1924 (2014) 


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



2013 
Coons M, 'Transcendental solutions of a class of minimal functional equations', Canadian Mathematical Bulletin. Bulletin Canadien de MathÃ©matiques, 56 283291 (2013) [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]



2012 
Bell JP, Bruin N, Coons M, 'Transcendence of generating functions whose coefficients are multiplicative', Transactions of the American Mathematical Society, 364 933959 (2012) [C1]



2012 
Coons M, 'Extension of some theorems of W. Schwarz', Canadian Mathematical Bulletin. Bulletin Canadien de MathÃ©matiques, 55 6066 (2012) [C1]



2012 
Coons M, 'A note on two conjectures associated to Goldbach's problem', Publicationes Mathematicae Debrecen, 80 343345 (2012) [C1]



2012 
Coons M, Vrbik P, 'An irrationality measure for regular paperfolding numbers', Journal of Integer Sequences, 15 (2012) [C1]



2012 
Coons M, 'A correlation identity for Stern's sequence', Integers, 12 459464 (2012) [C1]



2011 
Coons M, 'On some conjectures concerning Stern's sequence and its twist', Integers, 11 775789 (2011) [C1]



2011 
Coons M, Shallit J, 'A pattern sequence approach to Stern's sequence', Discrete Mathematics, 311 26302633 (2011) [C1]



2011 
Coons M, Dahmen SR, 'On the residue class distribution of the number of prime divisors of an integer', Nagoya Mathematical Journal, 202 1522 (2011) [C1]



2010 
Coons M, 'The transcendence of series related to Stern's diatomic sequence', International Journal of Number Theory, 6 211217 (2010) [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 Allou... [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 8 n=1 Â¿(n) X n e F p [[X]] is transcendental over F p (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.



2010 
Borwein P, Choi SKK, Coons M, 'Completely multiplicative functions taking values in $1,1$', Transactions of the American Mathematical Society, 362 62796291 (2010) [C1]



2009 
Borwein P, Coons M, 'Transcendence of power series for some number theoretic functions', Proceedings of the American Mathematical Society, 137 13031305 (2009) [C1]



2009 
Coons M, Kirsten K, 'General moment theorems for nondistinct unrestricted partitions', Journal of Mathematical Physics, 50 01351719 (2009) [C1]


