La constant de Bruijn-Newman

Abstract

[en] One of the most famous conjectures from number theory is the Riemann hipothesis. This conjecture has been studied from different branches of mathematics but unfortunately even today is not resolved. A way of study the behaviour of the zeros of the Riemann zeta function is by studying the de Bruijn-Newman constant. This work has as a goal to understand some results about this constant. We explain the results that lead to this constant, we see the relation between the constant and the Riemann Hipothesis and other results. Our main goal is to comprehend the article of George Csordas, Wayne Smith i Richard S. Varga, one of the most important contributions about the de Bruijn-Newman constant.