S. Wakatsuki

activity

20132026

most citedOn the geometric side of the Arthur trace formula for the symplectic group of rank 2

9 citations · 26 across the 17 of their papers we have counts for

collaborators

18 papers

math.RT2026

On the absolute convergence of the spectral side of the twisted trace formula

Werner Müller, Satoshi Wakatsuki

We establish the absolute convergence of the spectral side of the twisted trace formula for reductive algebraic groups. More precisely, we extend the absolute convergence theorem o…

math.NT2026

The Eichler--Selberg trace formula for Hilbert cusp forms, the class numbers of quartic CM fields, and their distributions

Seiji Kuga, Andrei Seymour-Howell, Satoshi Wakatsuki

Motivated by Su's construction of Cohen-type Eisenstein series of half-integral weight over totally real number fields \cite{Su16}, we introduce a generalization of Hurwitz class n…

math.NT2024

Asymptotic behavior for twisted traces of self-dual and conjugate self-dual representations of $GL_{n}$

Yugo Takanashi, Satoshi Wakatsuki

In this paper, we study the asymptotic behavior of the sum of twisted traces of self-dual or conjugate self-dual discrete automorphic representations of $GL_{n}$ for the lev…

math.NT2023

Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant $2$

Hiroyuki Ochiai, Satoshi Wakatsuki, Shun'ichi Yokoyama

In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant $2$ , and p…

math.NT2023

Non-vanishing theorems for prime twists of some modular $L$ -functions

Masataka Chida, Satoshi Wakatsuki

In this paper, we give some non-vanishing results on the central values of prime twists of modular $L$ -functions by imaginary quadratic fields for specific elliptic modular forms.…

math.NT2022★ 2 cited

Distribution of toric periods of modular forms on definite quaternion algebras

Miyu Suzuki, Satoshi Wakatsuki, Shun'ichi Yokoyama

Let $D$ be a definite quaternion algebra over $Q$ and $O$ an Eichler order in $D$ of square-free level. We study distribution of the toric periods of algebraic m…

math.NT2021★ 2 cited

Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

We prove equidistribution theorems for a family of holomorphic Siegel cusp forms of general degree in the level aspect. Our main contribution is to estimate unipotent contributions…

math.NT2021

Explicit mean value theorems for toric periods and automorphic $L$ -functions

Miyu Suzuki, Satoshi Wakatsuki

Let $F$ be a number field and $D$ a quaternion algebra over $F$ . Take a cuspidal automorphic representation $π$ of $D_{A}^{\times}$ with trivial central character and a cusp…

math.NT2020

Zeta functions and nonvanishing theorems for toric periods on $GL_{2}$

Miyu Suzuki, Satoshi Wakatsuki

Let $F$ be a number field and $D$ a quaternion algebra over $F$ . Take a cuspidal automorphic representation $π$ of $D_{A}^{\times}$ with trivial central cahracter. We study th…

math.NT2020

Asymptotics for Hecke eigenvalues of automorphic forms on compact arithmetic quotients

Pablo Ramacher, Satoshi Wakatsuki

In this paper, we describe the asymptotic distribution of Hecke eigenvalues in the Laplace eigenvalue aspect for certain families of Hecke-Maass forms on compact arithmetic quotien…

math.NT2019

Mass formulas and Eisenstein congruences in higher rank

Kimball Martin, Satoshi Wakatsuki

We use mass formulas to construct minimal parabolic Eisenstein congruences for algebraic modular forms on reductive groups compact at infinity, and study when these yield congruenc…

math.NT2019★ 1 cited

The Shintani double zeta functions

Henry H. Kim, Masao Tsuzuki, Satoshi Wakatsuki

In this paper, we give an explicit formula of the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three a…

math.NT2018★ 1 cited

Equidistribution theorems for holomorphic Siegel modular forms for $GS p_{4}$ ; Hecke fields and $n$ -level density

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

This paper is a continuation of the author's previous wotk. We supplement four results on a family of holomorphic Siegel cusp forms for $GS p_{4} / Q$ . First, we improve the re…

math.NT2017

The subregular unipotent contribution to the geometric side of the Arthur trace formula for the split exceptional group $G_{2}$

Tobias Finis, Werner Hoffmann, Satoshi Wakatsuki

In this paper, a zeta integral for the space of binary cubic forms is associated with the subregular unipotent contribution to the geometric side of the Arthur trace formula for th…

math.NT2017★ 5 cited

Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups

Pablo Ramacher, Satoshi Wakatsuki

Let $H$ be a semisimple algebraic group, $K$ a maximal compact subgroup of $G := H (R)$ , and $Γ \subset H (Q)$ a congruence arithmetic subgroup. In this paper, we gene…

math.NT2016★ 5 cited

An equidistribution theorem for holomorphic Siegel modular forms for $GS p_{4}$

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $GS p_{4} / Q$ in various aspects. A main tool is Arthur's invariant trace formula. While…

math.NT2016★ 1 cited

The dimensions of spaces of Siegel cusp forms of general degree

Satoshi Wakatsuki

In this paper, we give a dimension formula for spaces of Siegel cusp forms of general degree with respect to neat arithmetic subgroups. The formula was conjectured before by severa…

math.NT2013★ 9 cited

On the geometric side of the Arthur trace formula for the symplectic group of rank 2

Werner Hoffmann, Satoshi Wakatsuki

We study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group or the split symplectic group of rank 2 over any algeb…

On the absolute convergence of the spectral side of the twisted trace formula

The Eichler--Selberg trace formula for Hilbert cusp forms, the class numbers of quartic CM fields, and their distributions

Asymptotic behavior for twisted traces of self-dual and conjugate self-dual representations of GLn​

Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant 2

Non-vanishing theorems for prime twists of some modular L-functions

Distribution of toric periods of modular forms on definite quaternion algebras

Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

Explicit mean value theorems for toric periods and automorphic L-functions

Zeta functions and nonvanishing theorems for toric periods on GL2​

Asymptotics for Hecke eigenvalues of automorphic forms on compact arithmetic quotients

Mass formulas and Eisenstein congruences in higher rank

The Shintani double zeta functions

Equidistribution theorems for holomorphic Siegel modular forms for GSp4​; Hecke fields and n-level density

The subregular unipotent contribution to the geometric side of the Arthur trace formula for the split exceptional group G2​

Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups

An equidistribution theorem for holomorphic Siegel modular forms for GSp4​

The dimensions of spaces of Siegel cusp forms of general degree

On the geometric side of the Arthur trace formula for the symplectic group of rank 2

Asymptotic behavior for twisted traces of self-dual and conjugate self-dual representations of $GL_{n}$

Computations of algebraic modular forms associated with the definite quaternion algebra of discriminant $2$

Non-vanishing theorems for prime twists of some modular $L$ -functions

Explicit mean value theorems for toric periods and automorphic $L$ -functions

Zeta functions and nonvanishing theorems for toric periods on $GL_{2}$

Equidistribution theorems for holomorphic Siegel modular forms for $GS p_{4}$ ; Hecke fields and $n$ -level density

The subregular unipotent contribution to the geometric side of the Arthur trace formula for the split exceptional group $G_{2}$

An equidistribution theorem for holomorphic Siegel modular forms for $GS p_{4}$