Shingo Sugiyama

activity

20212024

collaborators

3 papers

math.NT2024

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…

math-ph2023

Lattice sums of $I$ -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 $I$ -Bessel functions on lattices, previously given by G. Chinta, J. Jorgenson, A. Karlsson and M. Neuhauser. Moreover we prove tha…

math.NT2021

Low-lying zeros of symmetric power $L$ -functions weighted by symmetric square $L$ -values

Shingo Sugiyama

For a totally real number field $F$ and its adèle ring $A_{F}$ , let $π$ vary in the set of irreducible cuspidal automorphic representations of $PGL_{2} (A_{F})$ co…

Integrality of Hecke eigenvalues and the growth of Hecke fields

Lattice sums of I-Bessel functions, theta functions, linear codes and heat equations

Low-lying zeros of symmetric power L-functions weighted by symmetric square L-values

Lattice sums of $I$ -Bessel functions, theta functions, linear codes and heat equations

Low-lying zeros of symmetric power $L$ -functions weighted by symmetric square $L$ -values