Preprint
Oct 2026
Upper Bounds on the de Bruijn-Newman constant for Dirichlet $L$-functions with primitive real-valued characters
Let $\chi_m$ be a primitive real-valued Dirichlet character of conductor $m\ge3$, let $L(s)=L(s,\chi_m)$ be the associated Dirichlet $L$-function, and let $\xi_L(s)$ denote its completed form. For each $t \in \mathbb R,$ we define the entire function \[ H^L_t(z) := \int_{-\infty}^{\infty} e^{tu^2}\, \Phi_L(u)\, e^{izu}...
R. Freire, Cristian Gonz'alez-Riquelme, Claudio Muñoz et al.
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