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- Title
On signs of Hecke eigenvalues of Siegel eigenforms.
- Authors
Kumar, Arvind; Meher, Jaban; Shankhadhar, Karam Deo
- Abstract
In this article, we distinguish Siegel cuspidal eigenforms of degree two on the full symplectic group from the signs of their Hecke eigenvalues. To establish our theorem, we obtain a result towards simultaneous sign changes of eigenvalues of two Siegel eigenforms. In the course of the proof, we also prove that the Satake p‐parameters of two different Siegel eigenforms are distinct for a set of primes p of density 1. The main ingredient to prove the latter result is the theory of Galois representations attached to Siegel eigenforms.
- Subjects
EIGENVALUES; SYMPLECTIC groups; GALOIS theory; REPRESENTATION theory
- Publication
Mathematika, 2022, Vol 68, Issue 4, p1030
- ISSN
0025-5793
- Publication type
Article
- DOI
10.1112/mtk.12154