The Laguerre-Pólya class theory of functions and applications in the Analytic Number Theory

• Grant number: 17/15223-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2017
• End date: September 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Dimitar Kolev Dimitrov
• Grantee: Willian Diego Oliveira
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 16/09906-0 - Harmonic analysis, approximation theory and applications, AP.TEM

Abstract

The principal aim of this project is to study conditions for an entire function defined as a Fourier transform of a positive kernel to possess only real zeros. A special case inspired naturally by the properties of the Riemann xi-function is when the kernel is related to a modular or a quasi-modular form.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

OLIVEIRA, WILLIAN D.. Zeros of Dirichlet polynomials via a density criterion. JOURNAL OF NUMBER THEORY, v. 203, p. 80-94, OCT 2019. (13/14881-9, 17/15223-6, 16/09906-0)