Explicit estimates for the zeros of Hecke $L$-functions

Abstract

Let $K$ be a number field and, for an integral ideal $\mathfrak{q}$ of $K$, let $\chi$ be a character of the narrow ray class group modulo $\mathfrak{q}$. We establish various new and improved explicit results, with effective dependence on $K$, $\mathfrak{q}$ and $\chi$, regarding the zeros of the Hecke L-function $L(s,\chi )$, such as zero-free regions, Deuring-Heilbronn phenomenon, and zero density estimates.

53 pages, 14 tables; v4 contains corrections to equations (1.2) and (3.1) and the proof of Lemma 3.2; note the published version may differ slightly

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