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). If you would like one of my papers, and
no link is provided, please feel free to contact me and I will gladly email you a copy.
preprints
| 62. | (with J. Lind) Radial asymptotics of generating functions of \(k\)-regular sequences.
| | 61. | (with S. Kristensen and M. L. Laursen) Asymptotics for partitions over the Fibonacci numbers and related sequences.
| | 60. | (with Y. Tachiya) Linear independence of series related to the Thue-Morse sequence over powers.
| | 59. | (with J. Evans, P. Gohlke and N. Manibo) Spectral theory of regular sequences: parametrisation and spectral classification.
|
published and accepted
| 58. | Towards a classification of regular sequences,
RIMS Kokyuroku, Analytic Number Theory and Related Topics (2023), to appear.
| | 57. | (with M. Baake) Correlations of the Thue-Morse sequence,
Indagationes Mathematicae, Special Issue on Aperiodic Order in honor of Uwe Grimm, to appear.
| | 56. | Some problems at the interface of number theory and aperiodic order,
Oberwolfach Reports 37 (2023), 18-21.
| | 55. | (with J. Evans, Z. Groth and N. Manibo) Zaremba, Salem, and the fractal nature of ghost distributions,
Bulletin of the Australian Mathematical Society 107 (2023), 374-389.
| | 54. | Measures associated to regular sequences and their characterisation,
Oberwolfach Reports 21 (2022), 1103-1104.
| | 53. | (with J. Evans and N. Manibo) Spectral theory of regular sequences,
Documenta Mathematica 27 (2022), 629-653.
| | 52. | (with M. Baake, J. Evans and P. Gohlke) On a family of singular continuous measures related to the doubling map, Indagationes Mathematicae 32 (2021), no. 4, 847-860. pdf
| | 51. | (with M. Baake) Scaling of the diffraction measure of \(k\)-free integers near the origin,
Michigan Mathematical Journal 70 (2021), 213-221.
| | 50. | A diffraction abstraction,
in "2019-20 MATRIX Annals", 735-744 MATRIX Book Ser. 4, Springer, 2021.
| | 49. | (with M. Baake, U. Grimm, J. A. G. Roberts and R. Yassawi) Aperiodic order meets number theory: Origin and structure of the field, in "2019-20 MATRIX Annals", 663-667, MATRIX Book Ser. 4, Springer, 2021. pdf
| | 48. | (with J. Evans) A sequential view of self--similar measures, or, what the ghosts of Mahler and Cantor can teach us about dimension, Journal of Integer Sequences 24 (2021), Article 21.2.5, 1-10. pdf
| | 47. | Degree-one Mahler functions: asymptotics, applications and speculations,
Bulletin of the Australian Mathematical Society 102 (2020), no. 3, 399-409.
| | 46. | (with M. Baake and N. Manibo) Constant-length binary substitutions and Mahler measures of Borwein polynomials, in ``From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M.~Borwein'', 303--322, Springer Proceedings in Math. & Stat., Vol. 13, Springer, 2020. pdf
| | 45. | (with Y. Bugeaud) A Mahler Miscellany, in "The Legacy of Kurt Mahler: A Mathematical Selecta",
Documenta Mathematica (2019), Extra Vol., Mahler Selecta, 179-190. pdf
| | 44. | (with M. Baake, J. M. Borwein and Y. Bugeaud) Introduction,
Documenta Mathematica (2019), Extra Vol., Mahler Selecta, 3-11. pdf
| | 43. | (co-edited with M. Baake and Y. Bugeaud) The Legacy of Kurt Mahler: A Mathematical Selecta,
Documenta Mathematica (2019), Extra Vol., Mahler Selecta. pdf
| | 42. | (with J. P. Bell, F. Chyzak and P. Dumas) Becker's conjecture on Mahler functions,
Transactions of the American Mathematical Society 372 (2019), no. 5, 3405-3423. pdf
| | 41. | (with L. Spiegelhofer) Number theoretic aspects of regular sequences,
in "Sequences, Groups, and Number Theory", 37-87, Trends Math., Birkhäuser/Springer, 2018. pdf
| | 40. | Mahler takes a regular view of Zaremba,
Special Volume in Honor of Jeffrey Shallit on the Occasion of His 60th Birthday,
Integers 18A (2018), #A6, 1-15. pdf
| | 39. | (with M. Baake) A natural probability measure derived from Stern's diatomic sequence,
Acta Arithmetica 183 (2018), no. 1, 87-99. pdf
| | 38. | Proof of Northshield's conjecture concerning an analogue of Stern's sequence for \(\mathbb{Z}[\sqrt{2}]\),
Australasian Journal of Combinatorics 71(1) (2018), 113-120. pdf AJC
| | 37. | Extension of a theorem of Duffin and Schaeffer,
Journal of Integer Sequences 20 (2017), Article 17.9.4, 1-4. pdf
| | 36. | An asymptotic approach in Mahler's method,
New Zealand Journal of Mathematics 47 (2017), 27-42. pdf
| | 35. | (with Y. Tachiya) Transcendence over meromorphic functions,
Bulletin of the Australian Mathematical Society 95 (2017), no. 3, 393-399. BAustMS
| | 34. | Regular sequences and the joint spectral radius,
International Journal of Foundations of Computer Science 28 (2017), no. 2, 135-140. pdf
| | 33. | (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
| | 32. | (with J. P. Bell) Transcendence tests for Mahler functions,
Proceedings of the American Mathematical Society 145 (2017), no. 3, 1061-1070. pdf
| | 31. | A Problem With A Regular Outlook,
Notes of the Canadian Mathematical Society 49 (2017), no. 1, 14-15. |
| 30. | Zero order estimates for Mahler functions,
New Zealand Journal of Mathematics 46 (2016), 83-88. pdf NZJM
| | 29. | (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
| | 28. | (with E. Catt and J. Velich) Strong normality and generalised Copeland-Erdős numbers,
Integers 16 (2016), #A11, 1-10. pdf
| | 27. | (with Bell and Hare) Growth degree classification for finitely generated semigroups of integer matrices,
Semigroup Forum 92 (2016), no. 1, 23-44. pdf
| | 26. | (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
| | 25. | (with H. Winning) Powers of two modulo powers of three,
Journal of Integer Sequences 18 (2015), Article 15.6.1, 1-9. JIS
| | 24. | (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
| | 23. | 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
|
| 22. | (with J. Borwein and Y. Bugeaud) The Legacy of Kurt Mahler,
Notices of the American Mathematical Society 62 (2015), no. 5, 526-531. |
| 21. | (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
| | 20. | (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
| | 19. | An arithemtical excursion via Stoneham numbers,
Journal of the Australian Mathematical Society 96 (2014), no. 3, 303-315. pdf
|
| 18. | (with J. Borwein and Y. Bugeaud) The Legacy of Kurt Mahler,
Australian Mathematical Society Gazette 41 (2014), no. 1, 11-21. |
| 17. | (with J. Borwein and Y. Bugeaud) The Legacy of Kurt Mahler,
Newsletter of the European Mathematical Society (2014), March Issue, 19-24. 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
| 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. |
|