Updated on 2021/10/20

写真a

 
MATSUSAKA Toshiki
 
Organization
Institute for Advanced Research Designated assistant professor
Graduate School of Mathematics Designated assistant professor
Title
Designated assistant professor

Degree 1

  1. PhD (Mathematics) ( 2019.3   Kyushu University ) 

Research Interests 2

  1. Number Theory

  2. Mock modular forms

Research Areas 1

  1. Natural Science / Algebra  / Number Theory

Research History 4

  1. Nagoya University   Institute for Advanced Research   Designated assistant professor

    2020.4

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    Country:Japan

  2. Kyushu University   Faculty of Mathematics   Researcher

    2019.4 - 2020.3

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    Country:Japan

  3. Kyushu University   JSPS Research Fellow (DC1)   Researcher

    2018.4 - 2019.3

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    Country:Japan

  4. Universität zu Köln (Germany)   Overseas Challenge Program for Young Researchers

    2018.4 - 2018.10

Education 3

  1. Kyushu University   Graduate School of Mathematics (doctor course)   Mathematics

    2018.4 - 2019.3

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    Country: Japan

  2. Kyushu University   Graduate School of Mathematics (master course)   Mathematics

    2016.4 - 2018.3

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    Country: Japan

  3. Kyushu University   School of Science   Mathematics

    2012.4 - 2016.3

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    Country: Japan

Professional Memberships 1

  1. The Mathematical Society of Japan

    2020.10

Awards 3

  1. 学術研究活動表彰

    2019.3   九州大学春季学位記授与式  

    松坂 俊輝

  2. 九州若手数学賞

    2019.2   日本数学会九州支部会  

    松坂 俊輝

  3. 九州若手数学者発表賞

    2018.2   日本数学会九州支部会  

    松坂俊輝

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    Award type:Award from Japanese society, conference, symposium, etc.  Country:Japan

 

Papers 11

  1. On the combinatorics of symmetrized poly-Bernoulli numbers Reviewed International coauthorship

    Beáta Bényi, Toshiki Matsuaka

    The Electronic Journal of Combinatorics   Vol. 28 ( 1.47 ) page: 1 - 20   2021

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  2. Linear Diophantine equations in Piatetski-Shapiro sequences Reviewed

    Toshiki Matsusaka, Kota Saito

    Acta Arithmetica   Vol. 200 ( 1 ) page: 91 - 110   2021

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  3. Ramanujan’s mock theta functions and mock modular forms Invited Reviewed

    Toshiki Matsusaka

    RIMS Kokyuroku Bessatsu, Algebraic Number Theory and Related Topics 2020   Vol. accepted   2021

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    Authorship:Lead author, Last author, Corresponding author   Language:English  

  4. Symmetrized poly-Bernoulli numbers and combinatorics Reviewed

    Toshiki Matsusaka

    Journal of Integer Sequences   Vol. 23 ( 9 ) page: 1 - 8   2020

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    Scopus

  5. Polyharmonic weak Maass forms of higher depth for SL_2(Z) Reviewed

    Toshiki Matsusaka

    The Ramanujan Journal   Vol. 51 ( 1 ) page: 19 - 42   2020

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  6. The Fourier coefficients of the McKay-Thompson series and the traces of CM values, an announcement Reviewed

    Toshiki Matsusaka

    RIMS Kokyuroku Bessatsu   Vol. B77   page: 259 - 263   2020

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  7. Traces of CM values and cycle integrals of polyharmonic Maass forms Reviewed

    Toshiki Matsusaka

    Research in Number Theory   Vol. 5   page: 1 - 25   2019

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  8. Fourier coefficients of polyharmonic weak Maass forms

    Toshiki Matsusaka

    PhD thesis, Kyushu University     2019

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Doctoral thesis  

  9. Real zeros of the Hurwitz zeta function Reviewed

    Toshiki Matsusaka

    Acta Arithmetica   Vol. 183 ( 1 ) page: 53 - 62   2018

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  10. The Fourier coefficients of the McKay-Thompson series and the traces of CM values Reviewed

    Toshiki Matsusaka

    Research in Number Theory   Vol. 3   page: 1 - 16   2017

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

  11. Arithmetic formulas for the Fourier coefficients of Hauptmoduln of level 2, 3, and 5 Reviewed

    Toshiki Matsusaka, Rhotaro Osanai

    Proceedings of the American Mathematical Society   Vol. 145 ( 4 ) page: 1383 - 1392   2017

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

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MISC 10

  1. 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

    松坂俊輝

    研究集会「結び目の数理III」報告集     2021

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    Authorship:Lead author, Last author, Corresponding author   Language:Japanese   Publishing type:Internal/External technical report, pre-print, etc.  

  2. Bijective enumerations for symmetrized poly-Bernoulli polynomials

    Minoru Hirose, Toshiki Matsusaka, Ryutaro Sekigawa, Hyuga Yoshizaki

    arXiv:2107.11952     2021

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    Language:English   Publishing type:Internal/External technical report, pre-print, etc.  

  3. Modular knots, automorphic forms, and the Rademacher symbols for triangle groups

    Toshiki Matsusaka, Jun Ueki

    arXiv:2109.01114     2021

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    Language:English  

  4. Extensions of the combinatorics of poly-Bernoulli numbers

    Beáta Bényi, Toshiki Matsusaka

    arXiv:2106.05585     2021

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    Language:English   Publishing type:Internal/External technical report, pre-print, etc.  

  5. A Hyperbolic Analogue of the Rademacher Symbol

    Toshiki Matsusaka

    arXiv:2003.12354     2020

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Internal/External technical report, pre-print, etc.  

  6. On the behavior of multiple zeta-functions with identical arguments on the real line

    Kohji Matsumoto, Toshiki Matsusaka, Ilija Tanackov

    arXiv:2012.01720     2020

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    Language:English   Publishing type:Internal/External technical report, pre-print, etc.  

  7. 二次形式とモックモジュラー形式

    松坂俊輝

    第15回数学総合若手研究集会テクニカルレポート     2019

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    Language:Japanese   Publishing type:Internal/External technical report, pre-print, etc.  

  8. 多重調和弱Maass形式のFourier係数

    松坂俊輝

    RIMS共同研究(公開型)「保型形式,保型表現とその周辺」数理解析研究所講究録     2019

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    Language:Japanese   Publishing type:Internal/External technical report, pre-print, etc.  

  9. フルヴィッツゼータ函数の実零点

    松坂俊輝

    第2回数理新人セミナー報告集     2019

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    Language:Japanese   Publishing type:Internal/External technical report, pre-print, etc.  

  10. Mock modular forms and polyharmonic Maass forms

    松坂俊輝

    2018早稲田整数論研究集会報告集     2018

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    Language:Japanese   Publishing type:Internal/External technical report, pre-print, etc.  

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Presentations 47

  1. Triangle modular knots and Rademacher symbols Invited

    Toshiki Matsusaka

    2021.9.3 

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    Event date: 2021.8 - 2021.9

    Presentation type:Oral presentation (invited, special)  

  2. サイクル積分とモックモジュラー形式に関する最近の進展 Invited

    松坂俊輝

    RIMS共同研究(公開型)「代数的整数論とその周辺」2020  2020.11.30 

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    Event date: 2020.11

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Zoom+RIMS(ハイブリッド)  

  3. Lifting maps for polyharmonic Maass forms Invited International conference

    Recent Advances and Applications of Modular Forms, AMS Sectional Meeting 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

  4. Extensions of the combinatorics of poly-Bernoulli numbers Invited

    Toshiki Matsusaka

    第56回関西多重ゼータ研究会  2021.10.23 

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    Event date: 2021.10

    Presentation type:Oral presentation (invited, special)  

  5. Bijective enumerations for symmetrized poly-Bernoulli polynomials Invited

    Toshiki Matsusaka

    九大多重ゼータセミナー  2021.10.18 

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    Event date: 2021.10

    Presentation type:Oral presentation (invited, special)  

  6. 中央二項級数に関するStephanの観察について

    Toshiki Matsusaka

    2021.10.13 

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    Event date: 2021.10

    Presentation type:Oral presentation (general)  

  7. 多重Bernoulli数の組合せ論 Invited

    Toshiki Matsusaka

    2021.10.2 

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    Event date: 2021.10

  8. Ramanujanのモックテータ関数とモックモジュラー形式について(サーベイ) Invited

    松坂俊輝

    東北大学代数セミナー  2021.6.23 

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    Event date: 2021.6

    Presentation type:Oral presentation (invited, special)  

  9. Stephan’s observation on the central binomial series Invited

    松坂俊輝

    九大多重ゼータセミナー  2021.6.4 

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    Event date: 2021.6

    Presentation type:Oral presentation (invited, special)  

  10. Ramanujanのモックテータ関数とモックモジュラー形式について(サーベイ) Invited

    松坂俊輝

    名古屋大学解析数論セミナー  2021.5.21 

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    Event date: 2021.5

    Presentation type:Oral presentation (invited, special)  

  11. Piatetski-Shapiro列における不定方程式の解について

    松坂俊輝

    九州代数的整数論2021春  2021.3.6 

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    Event date: 2021.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom+九州大学(ハイブリッド)  

  12. On the combinatorics of symmetrized poly-Bernoulli numbers

    松坂俊輝

    第14回ゼータ若手研究集会  2021.2.19 

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    Event date: 2021.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom  

  13. 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

    松坂俊輝

    研究集会「結び目の数理III」  2020.12.24 

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    Event date: 2020.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom  

  14. 対称化多重Bernoulli数の組合せ的解釈について Invited

    松坂俊輝

    津田塾大学整数論ワークショップ  2020.11.22 

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    Event date: 2020.11

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:Zoom  

  15. Two analogues of the Rademacher symbol Invited International conference

    Toshiki Matsusaka

    International Seminar on Automorphic Forms  2020.11.18 

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    Event date: 2020.11

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Zoom  

  16. Linking numbers and modular forms for the triangle groups Invited International conference

    Toshiki Matsusaka

    Japan Europe Number Theory Exchange Seminar  2020.11.10 

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    Event date: 2020.11

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Zoom  

  17. トーラス結び目と三角群のモックモジュラー形式

    松坂俊輝

    研究集会「東北結び目セミナー2020」  2020.10.17 

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    Event date: 2020.10

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom  

  18. アイゼンシュタイン級数の三幅対

    松坂俊輝

    日本数学会2020年度秋季総合分科会  2020.9.22 

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    Event date: 2020.9

    Language:Japanese   Presentation type:Oral presentation (general)  

  19. Rademacher 記号の双曲類似

    松坂俊輝

    第19回仙台広島整数論集会  2020.9.8 

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    Event date: 2020.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:Zoom  

  20. Eisenstein series associated to binary quadratic forms Invited International conference

    Toshiki Matsusaka

    九大多重ゼータセミナー  2020.7.13 

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    Event date: 2020.7

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Zoom  

  21. An explicit formula for the hyperbolic Rademacher symbol

    The 13th Young Mathematicians Conference on Zeta Functions 

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    Event date: 2020.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  22. アイゼンシュタイン級数の三幅対 Invited

    松坂俊輝

    九大代数学セミナー 

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    Event date: 2020.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  23. A Kronecker limit type formula for hyperbolic Eisenstein series Invited International conference

    Low dimensional topology and number theory XI 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  24. 二次形式とモックモジュラー形式

    松坂俊輝

    第15回数学総合若手研究集会 

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    Event date: 2019.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  25. 双曲型アイゼンシュタイン級数 Invited

    松坂俊輝

    第12回多重ゼータ研究集会&第44回関西多重ゼータ研究会(共同開催) 

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    Event date: 2019.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  26. 多重調和弱マース形式のフーリエ係数 Invited

    松坂俊輝

    第140回日本数学会九州支部例会 

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    Event date: 2019.2

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  27. Real zeros of the Hurwitz zeta function

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    Event date: 2019.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  28. Fourier coefficients of polyharmonic weak Maass forms

    RIMS conference "Automorphic forms, automorphic representations and related topics" 

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    Event date: 2019.1

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  29. Generating functions of CM & RM values

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    Event date: 2018.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  30. CM values, cycle integrals, and polyharmonic Maass forms Invited International conference

    Seminar der Arbeitsgruppe Algebra 

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    Event date: 2018.10

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  31. CM values, cycle integrals, and polyharmonic Maass forms Invited International conference

    Linfoot seminar 

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    Event date: 2018.10

    Language:English   Presentation type:Oral presentation (general)  

    Country:United Kingdom  

  32. Speed Talks International conference

    Conference on "Elementare und Analytische Zahlentheorie (ELAZ)" 

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    Event date: 2018.9

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  33. Traces of CM values and cycle integrals of polyharmonic Maass forms International conference

    4th EU/US Summer School + Workshop on Automorphic Forms and Related Topics 

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    Event date: 2018.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Hungary  

  34. Fourier coefficients of polyharmonic Maass forms International conference

    Number theory lunch seminar 

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    Event date: 2018.5

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  35. Mock modular forms and polyharmonic Maass forms Invited

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    Event date: 2018.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  36. 多重調和弱マース形式の構成

    松坂俊輝

    第138回日本数学会九州支部例会 

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    Event date: 2018.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  37. Polyharmonic weak Maass forms of higher depth for SL(2,Z) Invited International conference

    Trends in Modular Forms 

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    Event date: 2017.12

    Language:English   Presentation type:Oral presentation (general)  

    Country:Korea, Republic of  

  38. Arithmetic formulas for the coefficients of the McKay-Thompson series Invited International conference

    3rd Japanese-German Number Theory Workshop 

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    Event date: 2017.11

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  39. Traces of CM values of McKay-Thompson series International conference

    31st Automorphic Forms Workshop 

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    Event date: 2017.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:United States  

  40. 双対性を持つ多重ベルヌーイ数の和公式

    松坂俊輝

    第10回ゼータ若手研究集会 

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    Event date: 2017.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  41. Hurwitzゼータ函数の実零点

    松坂俊輝

    第10回多重ゼータ研究集会&第34回関西多重ゼータ研究会(共同開催) 

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    Event date: 2017.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  42. Formulas for the Fourier coefficients of genus zero modular functions

    RIMS Workshop, Algebraic Number Theory and Related Topics 

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    Event date: 2016.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  43. Traces of singular moduli and real analogues Invited International conference

    School on Mock Modular Forms and Related Topics 

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    Event date: 2016.11

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  44. Some formulas for the Fourier coefficients of Hauptmoduln of higher level

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    Event date: 2016.7

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  45. Fourier coefficients of Hauptmoduln and traces of singular moduli

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    Event date: 2016.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  46. Arithmetic formulas for the Fourier coefficients of modular functions of level 2, 3, and 5

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    Event date: 2016.6

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  47. 上指数が負の多重ベルヌーイ数の和について

    松坂俊輝

    APU多重ゼータ&モジュラーセミナー 

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    Event date: 2016.5

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

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KAKENHI (Grants-in-Aid for Scientific Research) 4

  1. モジュラー結び目が開く,数論的不変量と位相的不変量の新時代

    Grant number:21K18141  2021.7 - 2026.3

    日本学術振興会  科学研究費助成事業 挑戦的研究(開拓)  挑戦的研究(開拓)

    金子 昌信

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    Authorship:Coinvestigator(s) 

    Grant amount:\25870000 ( Direct Cost: \19900000 、 Indirect Cost:\5970000 )

  2. 非正則モジュラー形式の視点を用いた実二次体の数論

    Grant number:20K14292  2020.4 - 2024.3

    日本学術振興会  科学研究費助成事業  若手研究

    松坂 俊輝

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    Authorship:Principal investigator 

    Grant amount:\4030000 ( Direct Cost: \3100000 、 Indirect Cost:\930000 )

    モジュラー形式のフーリエ係数には,数論的に重要な情報が様々に現れる.これをカスプのまわりでの様子と見るならば,虚二次点や実二次点のまわりにおいては,どのような現象が見られるだろうか.本研究テーマは,ヘッケやピーターソンに由来するこの3種のフーリエ係数の数論的な役割について,この十数年の間に急速に進展している多種の非正則なモジュラー形式の理論を導入し,また相互に影響を与え発展させることで,その解明を目指すものである.

  3. モックモジュラー形式と楕円函数の実二次類似

    Grant number:18J20590  2018.4 - 2020.3

    日本学術振興会  科学研究費助成事業 特別研究員奨励費  特別研究員奨励費

    松坂 俊輝

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    Authorship:Principal investigator 

    DukeらはDirichlet L函数のs=1での特殊値の判別式に関する母函数を考えることで,モックモジュラー形式の拡張の一例を与えている.本研究ではLagarias-Rhoadesの仕事を踏まえることで,より一般に多重調和弱マース形式という非常に大きな函数のクラスを導入し,それらのなす空間の基底を具体的に決定,かつ基底の間に存在する,ある微分作用素による対応関係も明示的に記述した.これにより,Ono,Jeon-Kang-Kimらによって知られているモックモジュラー形式,およびその一般化の様々な例は,統一的に理解できるようになった.
    さて,本研究の目的の一つに「楕円モジュラーj函数の実二次点での「値」について理解する」を掲げていた.この値についてDukeらはまた,その適切な平均値を考えることで,その母函数がモックモジュラー形式になることを示している.これはZagierによるj函数のCM値に関する結果の実二次類似であるのだが,本研究ではj函数に限らず,一般の多重調和弱マース形式に対して,そのCM値や実二次点での値の適切な母函数が,半整数重さの保型性を持つことを明らかにした.これは従来の結果を大きく一般化するものであり,特にKroneckerの極限公式に適用することで,古典的に知られる等式の拡張・別証明を与えることができた.
    その他にも,Schwagenscheidtと共同で双曲型アイゼンシュタイン級数の極限公式を与えることに成功した.これは古典的な放物型アイゼンシュタイン級数に対応する類似物になっており,その極限公式の中にj函数の実二次点での値が現れることを確認した.一方で,この結果から得られる函数の一部を用いることで,ある絡み目の絡み数を計算できることが知られている.一見して異なる理論において共通する対象が現れており,これは本課題に何らかの示唆を与えるように思われる.

  4. 調和マース形式のフーリエ係数の数論的考察

    2018.4 - 2018.10

    日本学術振興会  若手研究者海外挑戦プログラム 

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    Authorship:Principal investigator 

 

Teaching Experience (On-campus) 3

  1. リーディングプログラム(PhD登龍門)YMコース

    2021

  2. 数学演習I

    2021

  3. 数学演習II

    2020