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

Asif Zaman

doi:10.1016/j.jnt.2015.10.003

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

Number Theory 2016-03-30 v4

Authors: Asif Zaman

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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.

Keywords

l-functions dirichlet characters

Cite

@article{arxiv.1502.05679,
  title  = {Explicit estimates for the zeros of Hecke $L$-functions},
  author = {Asif Zaman},
  journal= {arXiv preprint arXiv:1502.05679},
  year   = {2016}
}

Comments

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

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