# A Bessel delta-method and exponential sums for GL(2)

## TL;DR

This paper introduces a Bessel delta-method for exponential sums in GL(2), generalizing previous results and providing a concise proof of the Weyl-type subconvex bound for related L-functions.

## Contribution

It presents a new Bessel delta-method for GL(2) exponential sums and extends Jutila's results to more general holomorphic newforms, simplifying the proof of subconvex bounds.

## Key findings

- Generalized exponential sum estimates for holomorphic newforms
- Provided a short proof of the Weyl-type subconvex bound in the t-aspect
- Introduced a novel Bessel delta-method for GL(2) analysis

## Abstract

In this paper, we introduce a simple Bessel $\delta$-method to the theory of exponential sums for $\rm GL_2$. Some results of Jutila on exponential sums are generalized in a less technical manner to holomorphic newforms of arbitrary level and nebentypus. In particular, this gives a short proof for the Weyl-type subconvex bound in the $t$-aspect for the associated $L$-functions.