On the Lang–Trotter conjecture for Siegel modular forms
Abstract
Abstract Let be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with , generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues of , and obtain upper bounds for the sizes of the sets for fixed , in the spirit of the Lang–Trotter conjecture for elliptic curves.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Advanced Mathematical Identities
Publication details
- Journal / source
- Mathematika
- Publisher
- Wiley
- Volume
- 72
- Issue
- 3
- Publication date
- 3 June 2026
- Language
- EN