Eisenstein Congruences for SO(4, 3), SO(4, 4), Spinor, and Triple Product L-values

ABSTRACT

We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a split orthogonal group. We provide some numerical evidence in the case that the group is SO(4, 3) and the L-function is the spinor L-function of a genus 2, vector-valued, Siegel cusp form. We also consider the case that the group is SO(4, 4) and the L-function is a triple product L-function.

KEYWORDS:

• level one automorphic forms
• Eisenstein congruences
• critical L-values

Additional information

Funding

This work was supported by JSPS KAKENHI Grant Number 25247001.