10 citations · 30 across the 13 of their papers we have counts for
14 papers
One-level density of zeros of the Riemann zeta function weighted by its special values
Shingo Sugiyama, Ade Irma Suriajaya
We consider the one-level density of zeros of the Riemann zeta function weighted by its special values on the line , where is a fixed real number such that $1/2\…
Integrality of Hecke eigenvalues and the growth of Hecke fields
Kenji Sakugawa, Shingo Sugiyama
We prove that Hecke eigenvalues for any Hilbert and Siegel modular forms are algebraic integers. Our method does not rely on cohomologicality nor Galois representations. We apply t…
Lattice sums of -Bessel functions, theta functions, linear codes and heat equations
Takehiro Hasegawa, Hayato Saigo, Seiken Saito +1
We extend a certain type of identities on sums of -Bessel functions on lattices, previously given by G. Chinta, J. Jorgenson, A. Karlsson and M. Neuhauser. Moreover we prove tha…
A remark on the existence of equivariant functions
Shingo Sugiyama
Let be a Fuchsian group in . In this note, we discuss the existence of -equivariant functions for a two-dimensional representation of . This a…
Weighted one-level density of low-lying zeros of Dirichlet -functions
Shingo Sugiyama, Ade Irma Suriajaya
In this paper, we compute the one-level density of low-lying zeros of Dirichlet -functions in a family weighted by special values of Dirichlet -functions at a fixed $s \in [1…
Low-lying zeros of symmetric power -functions weighted by symmetric square -values
Shingo Sugiyama
For a totally real number field and its adèle ring , let vary in the set of irreducible cuspidal automorphic representations of co…
The limit theorem with respect to the matrices on non-backtracking paths of a graph
Takehiro Hasegawa, Takashi Komatsu, Norio Konno +4
We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the th moments of the arcsine law…
Optimal estimates for an average of Hurwitz class numbers
Shingo Sugiyama, Masao Tsuzuki
In this paper, we give an optimal estimate of an average of Hurwitz class numbers. As an application, we give an equidistribution result of the family $\{\frac{t}{2q^{ν/2}} \ | \ ν…
Quantitative non-vanishing of central values of certain -functions on
Shingo Sugiyama, Masao Tsuzuki
Let be an even Hecke-Maass cusp form on whose -function does not vanish at the center of the functional equation. In this article, we obtain an exac…
A quantum probabilistic approach to Hecke algebras for -adic
Takehiro Hasegawa, Hayato Saigo, Seiken Saito +1
The subject of the present paper is an application of quantum probability to -adic objects. We give a quantum-probabilistic interpretation of the spherical Hecke algebra for ${\…
An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
Shingo Sugiyama, Masao Tsuzuki
We give an exact formula of the average of adjoint -functions of holomorphic Hilbert cusp forms with a fixed weight and a square-free level, which is a generalization of Zagier'…
Existence of Hilbert cusp forms with non-vanishing -values
Shingo Sugiyama, Masao Tsuzuki
We give a derivative version of the relative trace formula on PGL(2) studied in our previous work, and obtain a formula of an average of central values (derivatives) of automorphic…
Asymptotic behaviors of means of central values of automorphic -functions for GL(2)
Shingo Sugiyama
Let be the adele ring of a totally real algebraic number field . We push forward an explicit computation of a relative trace formula for periods of automorphic form…
Relative trace formulas and subconvexity estimates of L-functions for Hilbert modular forms
Shingo Sugiyama, Masao Tsuzuki
We elaborate an explicit version of the relative trace formula on $\PGL(2)$ over a totally real number field for the toral periods of Hilbert cusp forms along the diagonal split to…