English

Zeros of Dirichlet Polynomials via a Density Criterion

Number Theory 2017-04-06 v1

Abstract

We obtain a necessary and sufficient condition in order that a semi-plane of the form (s)>r\Re(s)>r, rRr\in \mathbb{R}, is free of zeros of a given Dirichlet polynomial. The result may be considered a natural generalization of a well-known criterion for the truth of the Riemann hypothesis due to B\'aez-Duarte. An analog for the case of Dirichlet polynomials of a result of Burnol which is closely related to B\'aez-Duarte's one is also established.

Keywords

Cite

@article{arxiv.1704.01234,
  title  = {Zeros of Dirichlet Polynomials via a Density Criterion},
  author = {Willian D. Oliveira},
  journal= {arXiv preprint arXiv:1704.01234},
  year   = {2017}
}
R2 v1 2026-06-22T19:07:55.668Z