If $L(\chi ,1)=0$ then $\zeta (1/2+it)\ne 0$

Sergio Venturini

Let $L(s)={\sum }_{n=1}^{+\infty }\frac{a(n)}{n^s}$ be a Dirichlet series were $a(n)$ is a bounded completely multiplicative function. We prove that if $L(s)$ extends to a holomorphic…