Arithmetic behaviour of Hecke eigenvalues of Siegel cusp forms of degree two

Sanoli Gun; Winfried Kohnen; Biplab Paul

paper

Arithmetic behaviour of Hecke eigenvalues of Siegel cusp forms of degree two

arXiv:1901.10965

Abstract

Let $F$ and $G$ be Siegel cusp forms for $\Sp_4(\Z)$ and weights $k_{1}, k_{2}$ respectively. Also let $F$ and $G$ be Hecke eigenforms lying in distinct eigen spaces. Further suppose that neither $F$ nor $G$ is a Saito-Kurokawa lift. In this article, we study simultaneous arithmetic behaviour of Hecke eigenvalues of these Hecke eigenforms.

18 pages