Note on a hypothesis implying the non-vanishing of Dirichlet $L$-series $L(s,\chi )$ for $s>0$ and real characters $\chi $
Volume 96 / 2003
Colloquium Mathematicum 96 (2003), 207-212
MSC: Primary 11M20.
DOI: 10.4064/cm96-2-5
Abstract
We prove that if $\chi $ is a real non-principal Dirichlet character for which $L(1,\chi )\le 1-\mathop {\rm log}\nolimits 2$, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that $L(s,\chi )>0$ for $s>0$.
