Japanese/English

**WAKATSUKI Satoshi**

Professor, Faculty of Mathematics and Physics, Institute of Science and Engineering, Kanazawa University

Kakumamachi, Kanazawa, Ishikawa, 920-1192, Japan.

E-mail:

Research Interests: Automorphic form, Automorphic representation, Trace formula, Shintani zeta function, Automorphic period, Quaternion algebra, Quadratic form.

#### Papers

#### Proccedings

#### Graduate student's paper

#### Future Conferences

#### Past Conferences

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Professor, Faculty of Mathematics and Physics, Institute of Science and Engineering, Kanazawa University

Kakumamachi, Kanazawa, Ishikawa, 920-1192, Japan.

E-mail:

Research Interests: Automorphic form, Automorphic representation, Trace formula, Shintani zeta function, Automorphic period, Quaternion algebra, Quadratic form.

- Asymptotic behavior for twisted traces of self-dual and conjugate self-dual representations of GL_n (with Y. Takanashi), arXiv:2402.11945, 2024, submitted.
- Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant 2 (with H. Ochiai and S. Yokoyama), arXiv:2312.15893, revised on June 4th 2024, submitted.

Here is the database of bases of spaces of algebraic modular forms. - Non-vanishing theorems for prime twists of some modular L-functions (with M. Chida), arXiv:2310.19496, 2023, submitted.
- Explicit mean value theorems for toric periods and automorphic L-functions (with M. Suzuki, Appendix by authors and S. Yokoyama), arXiv:2103.04589, revised on June 5th 2024, submitted.
- Zeta functions and nonvanishing theorems for toric periods on GL_2 (with M. Suzuki), arXiv:2005.02017, revised on June 5th 2024, submitted.
- Distribution of Hecke eigenvalues for holomorphic Siegel modular forms (with H. Kim and T. Yamauchi), Acta Arithmetica 215 (2024), 161--177. link
- Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect (with H. Kim and T. Yamauchi), Algebra Number Theory 18 (2024), 993--1038. arXiv link
- Mass formulas and Eisenstein congruences in higher rank (with K. Martin), J. Number Theory 257 (2024), 249--272. arXiv link
- Distribution of toric periods of modular forms on definite quaternion algebras (with M. Suzuki and S. Yokoyama), Res. Number Theory 8 (2022), Article number: 90. arXiv link BEER

Here are some graphs for distributions of toric periods. - Asymptotics for Hecke eigenvalues of automorphic forms on compact arithmetic quotients (with P. Ramacher), Adv. Math. 404 Part A (2022), 108372. arXiv link
- The Shintani double zeta functions (with H. Kim and M. Tsuzuki), Forum Mathematicum 34 (2022), 469--505. arXiv link

The published version includes an appendix in which we explained prior works. - Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups (with P. Ramacher), Math. Z. 298 (2021), 1383--1424. arXiv link
- Equidistribution theorems for holomorphic Siegel modular forms for GSp_4; Hecke fields and n-level density (with H. Kim and T. Yamauchi), Math. Z. 295 (2020), 917--943. arXiv link
- An equidistribution theorem for holomorphic Siegel modular forms for GSp_4 (with H. Kim and T. Yamauchi), J. Inst. Math. Jussieu 19 (2020), 351--419. arXiv link
- The dimensions of spaces of Siegel cusp forms of general degree, Adv. Math. 340 (2018), 1012--1066. arXiv link
- The subregular unipotent contribution to the geometric side of the Arthur trace formula for the split exceptional group G_2 (with T. Finis and W. Hoffmann), Geometric Aspects of the Trace Formula, Proceedings of the Simons symposium, Schloss Elmau, Germany, April 10--April 16, 2016. Simons Symposia, 163--182 (2018). arXiv link
- On the geometric side of the Arthur trace formula for the symplectic group of rank 2 (with W. Hoffmann), Mem. Amer. Math. Soc. 255 (2018), no. 1224. arXiv link
- Congruences modulo 2 for dimensions of spaces of cusp forms, J. Number Theory 140 (2014), 169--180. link erratum
- Multiplicity formulas for discrete series representations in L
^{2}(Γ∖Sp(2,R)), J. Number Theory 133 (2013), 3394--3425. link - Dimension formulas for spaces of vector-valued Siegel cusp forms of degree two, J. Number Theory 132 (2012), 200--253. link
- Relations among Dirichlet series whose coefficients are class numbers of binary cubic forms, Amer. J. Math. 131 (2009), 1525--1541 (with Y. Ohno and T. Taniguchi). arXiv link
- Siegel modular forms of small weight and the Witt operator, Contemp. Math. 493 (2009), 189--209 (with T. Ibukiyama). link
- Igusa local zeta functions and integration formulas associated to equivariant maps, Osaka J. Math. 42 (2005), 463--486.
- The Igusa local zeta function of the simple prehomogeneous vector space (GL(1)
^{4}×SL(2n+1),Λ_{2}+Λ_{1}+Λ_{1}+Λ_{1}), J. Math. Soc. Japan 57 (2005), no. 1, 115--126. - Igusa local zeta functions of regular 2-simple prehomogeneous vector spaces of type I with universally transitive open orbits, Math. J. Okayama Univ. 46 (2004), 85--104.
- b-Functions of regular 2-simple prehomogeneous vector spaces associated to the symplectic group and the orthogonal group, Comment. Math. Univ. St. Pauli 53 (2004), no. 2, 121--137.

- Kazuki Oshita, Functional equations and gamma factors of local zeta functions for the metaplectic cover of SL_2 (with M. Tsuzuki), J. Number Theory 259 (2024), 57--81. arXiv link
- Chihiro Hiramoto, On the functional equations of the Shintani double zeta functions, Comment. Math. Univ. St. Pauli 70 (2022), 1--10. link

25th Autumn Workshop on Number Theory

Date: 28 (Mon.) -- Nov. 1 (Fri.) 2024.

Venue: Room 501, Science Building No.4, Hokkaido University

24th Autumn Workshop on Number Theory

Date: 30 (Mon.) -- Nov. 3 (Fri.) 2023.

Venue: Room 501, Science Building No.4, Hokkaido University

23rd Autumn Workshop on Number Theory

Date: Oct. 31 (Mon.) -- Nov. 4 (Fri.) 2022.

Venue: Kanazawa Chamber of Commerce Hall (from 31st to 3rd), Kanazawa University Satellite Plaza (4th)

RIMS Conference: Automorphic forms, automorphic representations and related topics

Date: Jan. 21 (Mon.) -- Jan. 25 (Fri.) 2019.

Venue: Room 420, RIMS, Kyoto University

Last modified: February 20, 2024