S. Wakatsuki

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20242026

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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.NT2025

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.NT2024

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 $I ¨ $ of $D_{A}^{\times}$ with trivial central character and a cus…

math.NT2024

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 $I ¨ $ of $D_{A}^{\times}$ with trivial central cahracter. We study t…

math.NT2024

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…

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​

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

Zeta functions and nonvanishing theorems for toric periods on GL2​

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

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

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

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

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