Explicit results on the distribution of zeros of Hecke $L$-functions

Abstract

We prove an explicit log-free zero density estimate and an explicit version of the zero-repulsion phenomenon of Deuring and Heilbronn for Hecke $L$-functions. In forthcoming work of the second author, these estimates will be used to establish explicit bounds on the least norm of a prime ideal in a congruence class group and improve upon existing explicit bounds for the least norm of a prime ideal in the Chebotarev density theorem.

32 pages

References in corpus (2)

• Explicit results on the distribution of zeros of Hecke $L$-functions
• Explicit estimates for the zeros of Hecke $L$-functions

Cited by in corpus (7)

• An explicit bound for the least prime ideal in the Chebotarev density theorem
• A Chebotarev variant of the Brun-Titchmarsh theorem and bounds for the Lang-Trotter conjectures
• Explicit results on the distribution of zeros of Hecke $L$-functions
• Explicit estimates for the zeros of Hecke $L$-functions
• On the least prime ideal and Siegel zeros
• The least unramified prime which does not split completely
• The Density of Numbers Represented by Diagonal Forms of Large Degree