On p-adic L-functions for ${\rm GL}(n)\times{\rm GL}(n-1)$ over totally real fields

TL;DR

This paper refines constructions of p-adic L-functions for Rankin-Selberg convolutions on GL(n)×GL(n-1) over totally real fields and proves an intrinsic functional equation, advancing the understanding of their arithmetic properties.

Contribution

It introduces an improved construction of p-adic L-functions for GL(n)×GL(n-1) and establishes a fundamental functional equation for these functions.

Findings

Refined p-adic L-function constructions for GL(n)×GL(n-1)

Proved an intrinsic functional equation for the p-adic L-functions

Enhanced understanding of the arithmetic properties of these L-functions

Abstract

We refine and extend previous constructions of $p$-adic $L$-functions for Rankin-Selberg convolutions on $\GL(n)\times\GL(n-1)$ for regular algebraic representations over totally real fields. We also prove an intrinsic functional equation for this $p$-adic $L$-function, which will be of interest in further study of its arithmetic properties.