Estimates of cusp forms for certain cocompact arithmetic subgroups

TL;DR

This paper provides a sub convexity estimate for Hecke eigen cusp forms on cocompact arithmetic subgroups, extending previous work on Maass forms with novel techniques and a holomorphic perspective.

Contribution

It introduces a new sub convexity estimate for holomorphic cusp forms, differing from prior methods used for Maass forms, advancing understanding in automorphic form bounds.

Findings

Derived a sub convexity estimate for holomorphic cusp forms

Extended the framework of Hecke eigenform bounds to cocompact groups

Compared techniques with previous approaches for Maass forms

Abstract

In this article, we derive a sub convexity estimate of Hecke eigen cusp forms associated to certain cocompact arithmetic subgroups of SL(2,R). The main result can be considered as the holomorphic version of the estimate of Hecke eigen Maass forms, derived in a famous paper of Iwaniec and Sarnak. A stronger estimate was derived by Khayutin and Steiner in arXiv:2009.07194. However, techniques used in both the papers are very different.