Upper Bounds on the de Bruijn-Newman constant for Dirichlet $L$-functions with primitive real-valued characters

Ricardo Freire, Cristian González-Riquelme, Claudio Muñoz +2

Let ${\chi }_m$ be a primitive real-valued Dirichlet character of conductor $m\ge 3$, let $L(s)=L(s,{\chi }_m)$ be the associated Dirichlet $L$-function, and let ${\xi }_L(s)$ denote its completed f…