L-functions with n-th order twists

TL;DR

This paper establishes a uniform subconvexity bound for a family of L-functions associated with n-th order characters over number fields, introducing a novel large sieve for these characters and deriving several key analytic results.

Contribution

It introduces a large sieve for n-th order characters and applies it to obtain subconvexity bounds, moment estimates, non-vanishing, and zero-density results for related L-functions.

Findings

Proved a uniform subconvexity bound for n-th order Hecke L-functions.

Derived a second moment estimate on the critical line.

Established non-vanishing and zero-density results for these L-functions.

Abstract

Let K be a number field containing the n-th roots of unity for some n > 2. We prove a uniform subconvexity result for a family of double Dirichlet series built out of central values of Hecke L-functions of n-th order characters of K. The main new ingredient, possibly of independent interest, is a large sieve for n-th order characters. As further applications of this tool, we derive several results concerning L(s,\chi) for n-th order Hecke characters: an estimate of the second moment on the critical line, a non-vanishing result at the central point, and a zero-density theorem.