Shingo Sugiyama

collaborators

3 papers

math.NT2026

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-ph2024

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.NT2024

A remark on the existence of equivariant functions

Shingo Sugiyama

Let $I^$ be a Fuchsian group in $SL_{2} (R)$ . In this note, we discuss the existence of $I ¨ $ -equivariant functions for a two-dimensional representation $I ¨ $ of $I^$ . Th…

Integrality of Hecke eigenvalues and the growth of Hecke fields

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

A remark on the existence of equivariant functions

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