On the size of $L(1,\chi)$ and S. Chowla's hypothesis implying that $L(1,\chi)>0$ for $s>0$ and for real characters $\chi$
Volume 130 / 2013
Colloquium Mathematicum 130 (2013), 79-90
MSC: Primary 11M20.
DOI: 10.4064/cm130-1-8
Abstract
We give explicit constants $\kappa$ such that if $\chi$ is a real non-principal Dirichlet character for which $L(1,\chi ) \le\kappa$, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that $L(s,\chi )>0$ for $s>0$. These constants are larger than the previous ones $\kappa =1-\log 2=0.306\ldots$ and $\kappa =0.367\ldots$ we obtained elsewhere.
