Large values of Hecke-Maass L-functions with prescribed argument

TL;DR

This paper explores the existence of large values of Hecke-Maass L-functions on the critical line with specific argument constraints, using advanced resonance methods to establish new results.

Contribution

It introduces a novel application of the resonance method to analyze large values of L-functions with prescribed argument, extending prior techniques.

Findings

Demonstrates the existence of large L-values with prescribed argument.

Extends resonance method applications to Maass form L-functions.

Provides new bounds and insights into L-function behavior.

Abstract

We investigate the existence of large values of L-functions attached to Maass forms on the critical line with prescribed argument. The results obtained rely on the resonance method developed by Soundararajan and furthered by Hough.