Geodesic
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 $\chi$
S. Louboutin1
1 Institut de Mathématiques de Luminy UMR 6206 163, avenue de Luminy Case 907 13288 Marseille Cedex 9, France
Colloquium Mathematicum, Tome 130 (2013) no. 1, pp. 79-90.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm130-1-8
Keywords: explicit constants kappa chi real non principal dirichlet character which chi kappa chowlas hypothesis satisfied cannot chowlas method proving chi these constants larger previous kappa log ldots kappa ldots obtained elsewhere

S. Louboutin 1

1 Institut de Mathématiques de Luminy UMR 6206 163, avenue de Luminy Case 907 13288 Marseille Cedex 9, France 
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S. Louboutin. 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 $\chi$. Colloquium Mathematicum, Tome 130 (2013) no. 1, pp. 79-90. doi : 10.4064/cm130-1-8. http://geodesic.mathdoc.fr/articles/10.4064/cm130-1-8/

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