GL(2) Weyl Bound via a multiplicative character delta method

Abstract

We use a trivial delta method with multiplicative characters for congruence detection to prove the Weyl bound for GL(2) in $t$-aspect for a holomorphic or Hecke-Maass cusp form of arbitrary level and nebentypus. This parallels the work of Aggarwal in 2018, with the difference being multiplicative character has a more natural connection to the twisted $L$-function. This provides another view point to understand and explore the trivial and other delta methods.

v3: 20 pages. Fixed minor typos and grammatical errors