michael coons' papers

Below is my list of publications; many of these can be found on the arXiv. There is also a section for my other contributions. The "pdf" link will take you to a preprint version of the article (this may not be the final version); a link with the journal initials will take you to the final version (when available).

preprints, in preparation, and in progress
(with M. Baake and N. Manibo) Constant-length binary substitutions and Mahler measures of Borwein polynomials, in preparation.
Proof of Northshield's conjecture concerning an analogue of Stern's sequence for \(\mathbb{Z}[\sqrt{2}]\),
preprint, 6 pages. pdf
(with M. Baake) A natural probability measure derived from Stern's diatomic sequence,
preprint, 12 pages. pdf
(co-edited with M. Baake, Y. Bugeaud and R. Quispel) A Mahler Selecta,
Documenta Mathematica, Book Series, in progress.

published or accepted
35. Mahler takes a regular view of Zaremba,
Integers, 15 pages, to appear. pdf
34. (with L. Spiegelhofer) Number theoretic aspects of regular sequences,
in ``Sequences, Groups, and Number Theory,'' Birkhauser/Springer, 50 pages, to appear. pdf
33. Extension of a theorem of Duffin and Schaeffer,
Journal of Integer Sequences 20 (2017), Article 17.9.4, 1-4. pdf
32. An asymptotic approach in Mahler's method,
New Zealand Journal of Mathematics 47 (2017), 27-42. pdf
31. (with Y. Tachiya) Transcendence over meromorphic functions,
Bulletin of the Australian Mathematical Society 95 (2017), no. 3, 393-399. BAustMS
30. Regular sequences and the joint spectral radius,
International Journal of Foundations of Computer Science 28 (2017), no. 2, 135-140. pdf
29. (with L. Spiegelhofer) The maximal order of hyper-(b-ary)-expansions,
Electronic Journal of Combinatorics 24 (2017), no. 1, #P1.15, 1-8. pdf EJC
28. (with J. P. Bell) Transcendence tests for Mahler functions,
Proceedings of the American Mathematical Society 145 (2017), no. 3, 1061-1070. pdf
27. Zero order estimates for Mahler functions,
New Zealand Journal of Mathematics 46 (2016), 83-88. pdf NZJM
26. (with M. Hussain and B. Wang) A dichotomy law for the Diophantine properties in β-dynamical systems,
Mathematika 62 (2016), no. 3, 884-897. pdf
25. (with E. Catt and J. Velich) Strong normality and generalised Copeland-Erdős numbers,
Integers 16 (2016), #A11, 1-10. pdf
24. (with Bell and Hare) Growth degree classification for finitely generated semigroups of integer matrices,
Semigroup Forum 92 (2016), no. 1, 23-44. pdf
23. (with R. P. Brent and W. Zudilin) Algebraic independence of Mahler functions via radial asymptotics,
International Mathematics Research Notices 2016 (2016), no. 2, 571-603. pdf
22. (with H. Winning) Powers of two modulo powers of three,
Journal of Integer Sequences 18 (2015), Article 15.6.1, 1-9. JIS
21. (with J. P. Bell and Y. Bugeaud) Diophantine approximation of Mahler numbers,
Proceedings of the London Mathematical Society (3) 110 (2015), no. 5, 1157-1206. pdf
20. Addendum to: On the rational approximation of the sum of the reciprocals of the Fermat numbers,
The Ramanujan Journal 37 (2015), no. 1, 109-111. pdf
19. (with J. Tyler) The maximal order of Stern's diatomic sequence,
Moscow Journal of Combinatorics and Number Theory 4 (2014), iss. 3, 3-13. pdf
18. (with J. P. Bell and K. G. Hare) The minimal growth of a k-regular sequence,
Bulletin of the Australian Mathematical Society 90 (2014), no. 2, 195-203. pdf
17. An arithemtical excursion via Stoneham numbers,
Journal of the Australian Mathematical Society 96 (2014), no. 3, 303-315. pdf
16. (with J. P. Bell and E. Rowland) The rational-transcendental dichotomy of Mahler functions,
Special Issue in Honour of the 60th Birthday of Jean-Paul Allouche
Journal of Integer Sequences 16 (2013), Article 13.2.10, 1-11. pdf
15. On the rational approximation of the sum of the reciprocals of the Fermat numbers,
The Ramanujan Journal 30 (2013), no. 1, 39-65. pdf RJ
14. Transcendental solutions of a class of minimal functional equations,
Canadian Mathematical Bulletin 56 (2013), no. 2, 283-291. CMB
13. A correlation identity for Stern's diatomic sequence,
Integers 12 (2012), #A3, 1-5. INTEGERS
12. A note on two conjectures associated to Goldbach's problem,
Publicationes Mathematicae Debrecen 80 (2012), 1-3.
11. (with J. P. Bell and N. Bruin) Transcendence of generating functions whose coefficients are multiplicative,
Transactions of the American Mathematical Society 364 (2012), no. 2, 933-959. pdf TAMS
10. (with P. Vrbik) An irrationality measure for paperfolding numbers,
Journal of Integer Sequences 15 (2012), Article 12.1.6, 1-10. JIS
9. Extension of some theorems of W. Schwarz,
Canadian Mathematical Bulletin 55 (2012), no. 1, 60-66. pdf CMB
8. (with J. Shallit) A pattern sequence approach to Stern's sequence,
Discrete Mathematics 311 (2011), 2630-2633. pdf DM
7. On some conjectures concerning Stern's sequence and its twist,
Integers 11 (2011), #A35, 1-14. INTEGERS
6. (with S. R. Dahmen) On the residue class distribution of the number of prime divisors of an integer,
Nagoya Mathematical Journal 202 (2011), 15-22. pdf NMJ
5. (Non)Automaticity of number theoretic functions,
Journal de Théorie des Nombres de Bordeaux 22 (2010), no. 2, 339-352. pdf JTNB
4. (with P. Borwein and S. K. K. Choi) Completely multiplicative functions taking values in \(\{-1,1\}\),
Transactions of the American Mathematical Society 362 (2010), no. 12, 6279-6291. pdf TAMS
3. The transcendence of series related to Stern's diatomic sequence,
International Journal of Number Theory 6 (2010), no. 1, 211-217. IJNT
2. (with P. Borwein) Transcendence of power series for some number theoretic functions,
Proceedings of the American Mathematical Society 137 (2009), no. 4, 1303-1305. pdf PAMS
1. (with K. Kirsten) General Moment Theorems for Non-Distinct Unrestricted Partitions,
Journal of Mathematical Physics 50 (2009), no. 1, 19 pages. pdf JMP

other written contributions
xiv. A Problem With A Regular Outlook,
Notes of the Canadian Mathematical Society 49 (2017), no. 1, 14-15.
xiii. (with J. Borwein and Y. Bugeaud) The Legacy of Kurt Mahler,
Notices of the American Mathematical Society 62 (2015), no. 5, 526-531.
xii. (with J. Borwein and Y. Bugeaud) The Legacy of Kurt Mahler,
Australian Mathematical Society Gazette 41 (2014), no. 1, 11-21.
xi. (with J. Borwein and Y. Bugeaud) The Legacy of Kurt Mahler,
Newsletter of the European Mathematical Society (2014), March Issue, 19-24. pdf
x. (with J. Borwein and Y. Bugeaud) The Kurt Mahler Archive,
a website dedicated to the mathematical life and collected works of Kurt Mahler, available here.
ix. On the multiplicative Erdős discrepancy problem,
(permanent preprint, not intended for publication). pdf
viii. Yet another proof of the infinitude of primes, I,
(permanent preprint, not intended for publication). pdf
vii. Hendrik Lenstra: Distinguished Lecture Series,
Fields Notes, Vol. 10:2 (2010), pages 3 and 14--15. pdf
vi. Workshop on Discovery and Experimentation in Number Theory,
Fields Notes, Vol. 10:2 (2010), pages 6 and 17. pdf
v. Some aspects of analytic number theory: parity, transcendence, and multiplicative functions,
Ph.D. Thesis, Simon Fraser University University, Burnaby, BC, 2009. pdf
iv. New proof of the equation \(\sum\mu(k)/k=0\),
Translation of Edmund Landau's Dissertation, preliminary version, preprint. pdf
iii. The Emergence of Modern Number Theory in Hungary,
Fulbright Student Conference Papers, TypoTEX Ltd. Electronic Publishing Co., Budapest, 2009,
181-192. preprint or published version
ii. General Moment Theorems with Applications,
Master's Thesis, Baylor University, Waco, TX, 2005. pdf
i. Numerical Methods for Left-Ventricular Contractility,
Bachelor's Thesis, The University of Montana, Missoula, MT, 2003.