論文等 (Publications)

論文 (Research Articles)  : arXiv (Toshiki Matsusaka)

1. A discretization of the iterated integral expression of the multiple polylogarithm (with Minoru Hirose and Shin-ichiro Seki), arXiv:2404.15210

2. On integrality and asymptotic behavior of the (k,l)-Göbel sequences (with Hibiki Gima, Taichi Miyazaki, Shunta Yara), arXiv:2402.09064

3. On finite analogues of Euler's constant (with Masanobu Kaneko and Shin-ichiro Seki), arXiv:2401.09935

4. Asymptotic coefficients of multiple zeta functions at the origin and generalized Gregory coefficients (with Hideki Murahara and Tomokazu Onozuka), arXiv:2312.14475.

5. Arithmetic Dijkgraaf-Witten invariants for real quadratic fields, quadratic residue graphs, and density formulas (with Yuqi Deng and Riku Kurimaru), Research in Number Theory 9, Article Number 70 (2023), (Link), (arXiv)

6. How long can k-Göbel sequences remain integers? (with Rinnosuke Matsuhira and Koki Tsuchida), accepted, The American Mathematical Monthly, arXiv:2307.09741.

7. Curious congruences for cyclotomic polynomials II (with Genki Shibukawa), Research in Number Theory, 10, Article Number 3 (2024), (Link), (arXiv)

8. Hikami’s observations on unified WRT invariants and false theta functions, accepted, "Low Dimensional Topology and Number Theory" Springer Proceedings in Mathematics & Statistics, arXiv:2212.06337.

9. Remarkable relations between the central binomial series, Eulerian polynomials, and poly-Bernoulli numbers, leading to Stephan's observation, (with Beáta Bényi), Kyushu Journal of Mathematics, vol 77, no. 1, (2023), 149--158. (Link), (arXiv)

10. Modular transformations of homological blocks for Seifert fibered homology 3-spheres (with Yuji Terashima), Communications in Mathematical Physics, 405 (2024), article number 48, (Link), (arXiv)

11. Modular knots, automorphic forms, and the Rademacher symbols for triangle groups (with Jun Ueki), Research in the Mathematical Sciences, 10 (2023), no.1, Paper No.4, (Link), (arXiv)

12. Bijective enumerations for symmetrized poly-Bernoulli polynomials (with Minoru Hirose, Ryutaro Sekigawa, Hyuga Yoshizaki), The Electronic Journal of Combinatorics, vol 29, 3, (2022), 1--18. (Link), (arXiv)

13. Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers (with Beáta Bényi), Journal de Théorie des Nombres de Bordeaux, Tome 34 (2022) no. 3, 917--939. (Link), (arXiv)

14. Ramanujan’s mock theta functions and mock modular forms (Japanese, survey), accepted, RIMS Kokyuroku Bessatsu, Algebraic Number Theory and Related Topics 2020. (PDF)

15. On the behavior of multiple zeta-functions with identical arguments on the real line (with Kohji Matsumoto and Ilija Tanackov), Journal of Number Theory, 239, (2022), 151--182. (Link) , (arXiv)

16. Linear Diophantine equations in Piatetski-Shapiro sequences (with Kota Saito), Acta Arithmetica, 200, 1 (2021), 91--110. (Link), (arXiv)

17. On the combinatorics of symmetrized poly-Bernoulli numbers (with Beáta Bényi), The Electronic Journal of Combinatorics, vol 28, 1, (2021), 1--20. (Link), (arXiv)

18. Symmetrized poly-Bernoulli numbers and combinatorics, Journal of Integer Sequences, 23 (2020), Article 20.9.2 (Link), (arXiv)

19. A Hyperbolic Analogue of the Rademacher Symbol, Mathematische Annalen, 388 (2024), 2843--2886 (Link), (arXiv)

20. Traces of CM values and cycle integrals of polyharmonic Maass forms, Research in Number Theory 5:8 (2019), 1--25. (Link), (arXiv)

21. Polyharmonic weak Maass forms of higher depth for SL_2(Z), The Ramanujan Journal, 51 (1) (2020), 19--42. (Link), (arXiv)

22. The Fourier coefficients of the McKay-Thompson series and the traces of CM values, an announcement, RIMS Kokyuroku Bessatsu, B77, Algebraic Number Theory and Related Topics 2016. (Link)

23. The Fourier coefficients of the McKay-Thompson series and the traces of CM values, Research in Number Theory 3 (2017), 1--16. (Link), (arXiv)

24. Real zeros of the Hurwitz zeta function, Acta Arithmetica, 183, 1 (2018), 53--62. (Link), (arXiv)

25. Arithmetic formulas for the Fourier coefficients of Hauptmoduln of level 2, 3, and 5 (with R. Osanai), Proc. Amer. Math. Soc. 145, (4) (2017), 1383--1392. (Link), (arXiv)

査読無し報告集など (Non-refereed Articles)

1. 円分多項式に関する奇妙な合同式について，RIMS共同研究（公開型）「解析的整数論とその周辺」(2023)，数理解析研究所講究録，PDF (日本語)

2. 葉廣級数と偽テータ関数に関する余録，2023早稲田整数論研究集会報告集, PDF (日本語)

3. マルコフの木，数学セミナー2023年9月号

4. テータ関数の2つの様式「擬テータ」と「偽テータ」, 第6回数理新人セミナー報告集 (2023), PDF (日本語)

5. 量子モジュラー形式とSeifert多様体に対するhomological blockの保型変換則, RIMS共同研究（公開型）「保型形式，保型L関数とその周辺」(2022), 数理解析研究所講究録, PDF (日本語)

6. 多重Bernoulli数の組合せ的解釈とStephanの観察について, RIMS共同研究（公開型）「解析的整数論とその周辺」(2021), 数理解析研究所講究録, PDF (日本語), 報告集全体はこちら (Link)

7. 三角群に関するRademacher記号とモジュラー結び目, 代数学シンポジウム報告集 (2021), PDF (日本語)，報告集全体はこちら (Link)

8. 三角群のモジュラー結び目に関するRademacher記号と2-コサイクルについて, 研究集会「結び目の数理III」報告集 (2021), PDF (日本語)，報告集全体はこちら (Link)

9. 多重調和弱Maass形式のFourier係数, RIMS共同研究(公開型)「保型形式，保型表現とその周辺」(2019), 数理解析研究所講究録, PDF (日本語)

10. フルヴィッツゼータ函数の実零点, 第2回数理新人セミナー報告集 (2019), PDF (日本語)

11. 二次形式とモックモジュラー形式, 第15回数学総合若手研究集会テクニカルレポート (2019), PDF (日本語)

12. Mock modular forms and polyharmonic Maass forms, 2018早稲田整数論研究集会報告集, PDF (日本語) 

その他 (Others)

1. 割れる？割れない？ゲーベルの不思議な数列, 九大理学部ニュース (2024年1月11日)

2. The Astonishing Behavior of Recursive Sequences, Quanta Magazine, November 16, 2023

3. 8, 24次元における最密球充填の証明を理解する, MATH POWER 2022の講演資料 (2022年9月24日)（PDF）

4. 2022年度八王子数論セミナー資料, 3rd orderモックテータ (PDF), 5th/7th orderモックテータ (PDF)

5. 素人的発想！フェルマーの方程式に解がある？, 九大理学部ニュース (2022年6月9日)

学位論文 (Theses)

• Fourier coefficients of polyharmonic weak Maass forms, (supervisor: Masanobu Kaneko), Ph.D. thesis, Kyushu University, 2019, PDF

• Several results on modular forms and zeta functions (in three parts), (supervisor: Masanobu Kaneko), Master's thesis, Kyushu University, 2018

Erdős number 3

Paul Erdős -- Aleksandar P. Ivić -- Kohji Matsumoto -- Toshiki Matsusaka