Shingo Sugiyama

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20212024

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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.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

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

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