Generating Functions on Covering Groups

TL;DR

This paper proves a conjecture that allows the meromorphic continuation of certain standard partial L-functions for genuine irreducible cuspidal representations on covering groups, advancing the understanding of their analytic properties.

Contribution

It proves Conjecture 1.2 from prior work, enabling the meromorphic continuation of standard partial L-functions on covering groups.

Findings

Proves Conjecture 1.2 in .

Establishes meromorphic continuation of L^S(s,).

Advances the theory of automorphic L-functions on covering groups.

Abstract

In this paper we prove Conjecture 1.2 in \cite{B-F}. This enables us to establish the meromorphic continuation of the standard partial $L$ function $L^S(s,\pi^{(n)})$. Here, $\pi^{(n)}$ is a genuine irreducible cuspidal representation of the group $GL_r^{(n)}({\bf A})$.