On Shalika models and p-adic L-Functions

TL;DR

This paper constructs p-adic L-functions for certain automorphic representations on GL(2n) with Shalika models using modular symbols and p-adic representation theory, offering a new systematic approach.

Contribution

It introduces a novel method leveraging p-adic group representation theory to build p-adic L-functions for automorphic representations with Shalika models.

Findings

Successful construction of p-adic L-functions for GL(2n) automorphic representations

Systematic use of p-adic group representation theory in L-function construction

Differentiates from previous methods by its representation-theoretic approach

Abstract

We use modular symbols to construct p-adic L-functions for cohomological cuspidal automorphic representations on GL(2n), which admit a Shalika model. Our construction differs from former ones in that it systematically makes use of the representation theory of p-adic groups.