Weyl bound for $\rm GL(2)$ in $t$-aspect via a trivial delta method

TL;DR

This paper proves the Weyl bound for L-functions of GL(2) cusp forms in the t-aspect using a trivial delta method, extending previous results to forms of arbitrary level and nebentypus.

Contribution

It introduces a trivial delta method approach to establish the Weyl bound for GL(2) L-functions in the t-aspect for forms of any level and nebentypus, broadening prior scope.

Findings

Weyl bound established for GL(2) L-functions in t-aspect.

Extension of previous results to arbitrary level and nebentypus.

Method provides a new approach to bounding L-functions in the t-aspect.

Abstract

We use a `trivial' delta method to prove the Weyl bound in $t$-aspect for the $\rm L$-function of a holomorphic or a Hecke-Maass cusp form of arbitrary level and nebentypus. In particular, this extends the results of Meurman and Jutila for the $t$-aspect Weyl bound, and the recent result of Booker, Milinovich and Ng to Hecke cusp forms of arbitrary level and nebentypus.