On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case

TL;DR

This paper establishes a Weyl-type subconvex bound for cube-free level Hecke characters over totally real fields, utilizing explicit inversion of Motohashi's formula and specialized Schwartz functions.

Contribution

It introduces a novel method for deriving subconvex bounds using explicit inversion of Motohashi's formula in the totally real case.

Findings

Proves a Weyl-type subconvex bound for cube-free Hecke characters.

Develops an explicit inversion technique for Motohashi's formula.

Highlights the role of specialized Schwartz functions in the proof.

Abstract

We prove a Weyl-type subconvex bound for cube-free level Hecke characters over totally real number fields. Our proof relies on an explicit inversion to Motohashi's formula. Schwartz functions of various kinds and the invariance of the relevant Motohashi's distributions discovered in a previous paper play central roles.