arXiv subjects

Seiji Kuga

Publications and source records attributed to Seiji Kuga.

4 recordsLinked to original sources

arXiv2026

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

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 numbers to totally real number fields. Using these generalized Hurwitz class numbers, we establish an Eichler--Selberg trace formula for the space of holomorphic Hilbert cusp forms over real quadratic fields of narrow class number one. While the classical Hurwitz class numbers are defined in terms of class numbers of imaginary quadratic fields, the generalized Hurwitz class numbers appearing in our Eichler--Selberg trace formula are defined in terms of class numbers of quartic CM fields. For applications of this Eichler--Selberg trace formula, we study the distribution of the generalized Hurwitz class numbers, prove class number relations, and carry out numerical computations of traces of Hecke operators for $\mathbb{Q}(\sqrt{5})$ and $\mathbb{Q}(\sqrt{29})$.

math.NT↗

arXiv2024

An asymptotic formula of spectral average of central $L$-values on ${\bf GSp}(2)$ for square free levels

We develop a new kind of relative trace formulas on ${\bf PGSp}_2$ involving the Bessel periods and the Rankin-Selberg type integral a la Piatetski-Shapiro for Siegel cusp forms on its spectral side. As an application, a version of weighted equidistribution theorems for the Satake parameters of Siegel cusp forms of square-free level and of scalar weights is proved.

math.NT↗

arXiv2024

The Ranking-Selberg integral on ${\bf GSp(2)}$ for square free levels

We explicitly compute the Rankin-Selberg type integral introduced by Piatetski-Shapiro over adeles for vector-valued Siegel cusp forms of square-free levels $\Gamma_0(N)$. On the way, for particular test functions in the Bessel models of irreducible admissible representations, exact evaluations of the local zeta-integrals are given.

math.NT↗

arXiv2018

Zeros of certain weakly holomorphic modular forms for the Fricke group $Γ_0^+(3)$

Let $M_k^!(Γ_0^+(3))$ be the space of weakly holomorphic modular forms of weight $k$ for the Fricke group of level $3$. We introduce a natural basis for $M_k^!(Γ_0^+(3))$ and prove that for almost all basis elements, all of their zeros in a fundamental domain lie on the circle centered at 0 with radius $\frac{1}{\sqrt{3}}$.

math.NT↗