Simple zeros of Dedekind zeta functions

Abstract

Using Stechkin's lemma we derive explicit regions of the half complex plane $\Re (s)\leq 1$ in which the Dedekind zeta function of a number field $K$ has at most one complex zero, this zero being real if it exists. These regions are Stark-like regions, i.e. given by all $s=\beta +i\gamma$ with $\beta\geq 1-c/\log d_K$ and $\vert\gamma\vert\leq d/\log d_K$ for some absolute positive constants $c$ and $d$. These regions are larger and our proof is simpler than recently published such regions and proofs.