Archimedean zeta integrals on U(n,1)

TL;DR

This paper explicitly computes archimedean zeta integrals for the unitary group U(n,1), linking automorphic representations to special values of L-functions, under the assumption of holomorphic discrete series.

Contribution

It provides explicit formulas for archimedean zeta integrals on U(n,1), advancing understanding of automorphic L-functions in this setting.

Findings

Explicit formulas for archimedean zeta integrals on U(n,1)

Connection between zeta integrals and automorphic L-values

Assumption of holomorphic discrete series for calculations

Abstract

For a dual pair of unitary groups with equal size, zeta integrals arising from Rallis inner product formula give the central values of certain automorphic L-functions. In this paper we explicitly calculate archimedean zeta integrals of this type for U(n,1), assuming that the corresponding archimedean component of the automorphic representation is a holomorphic discrete series.