arXiv subjects

Willian D. Oliveira

Publications and source records attributed to Willian D. Oliveira.

3 recordsLinked to original sources

arXiv2017

Zeros of Dirichlet Polynomials via a Density Criterion

We obtain a necessary and sufficient condition in order that a semi-plane of the form $\Re(s)>r$, $r\in \mathbb{R}$, 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 Báez-Duarte. An analog for the case of Dirichlet polynomials of a result of Burnol which is closely related to Báez-Duarte's one is also established.

math.NT↗

arXiv2016

An extremal problem related to generalizations of the Nyman-Beurling and Báez-Duarte criteria

We establish generalizations of the Nyman-Beurling and Báez-Duarte criteria concerning lack of zeros of Dirichlet $L$-functions in the semi-plane $\Re(s) >1/p$ for $p\in (1,2]$. We pose and solve a natural extremal problem for Dirichlet polynomials which take values one at the zeros of the corresponding $L$-function on the vertical line $\Re(s)=1/p$.

math.NT↗

arXiv2016

Sign regularity of Maclaurin coefficients of functions in the Laguerre-Pólya class

We prove that the signs of the Maclaurin coefficients of a wide class of entire functions that belong to the Laguerre-Pólya class posses a regular behaviour.

math.CV↗