Modular symbols for reductive groups and p-adic Rankin-Selberg convolutions over number fields

TL;DR

This paper constructs modular symbols for reductive groups and develops p-adic distributions that interpolate special values of Rankin-Selberg L-functions over number fields, advancing p-adic automorphic L-function theory.

Contribution

It introduces a broad class of modular symbols for reductive groups and constructs p-adic distributions for twisted Rankin-Selberg L-values over number fields.

Findings

Constructed modular symbols for reductive groups.

Developed p-adic distributions interpolating L-values.

Established boundedness and analyticity for ordinary representations.

Abstract

We give a construction of a wide class of modular symbols attached to reductive groups. As an application we construct a p-adic distribution interpolating the special values of the twisted Rankin-Selberg L-function attached to cuspidal automorphic representations of GL(n) and GL(n-1) over number fields. If the representations are ordinary at p, our distribution is bounded and yields analyticity of the associated p-adic L-function.