Certain L2-norms on automorphic representations of SL(2)

TL;DR

This paper investigates different L2-norms of automorphic representations of SL(2,R), providing bounds and comparisons that enhance understanding of L-function growth in a systematic framework.

Contribution

It introduces bounds for various L2-norms of automorphic representations of SL(2,R) and compares these norms to intrinsic representation norms, aiding in the analysis of L-function growth.

Findings

Bounded L2-norms of automorphic representations

Established relationships between different norms

Provided insights into L-function growth patterns

Abstract

Let $\Gamma$ be a non-uniform lattice in $SL(2, \mathbb R)$. In this paper, we study various $L^2$-norms of automorphic representations of $SL(2, \mathbb R)$. We bound these norms with intrinsic norms defined on the representation. Comparison of these norms will help us understand the growth of $L$-functions in a systematic way.