Geodesic
Note on a hypothesis implying the non-vanishing of Dirichlet $L$-series $L(s,\chi )$ for $s>0$ and real characters $\chi $
Stéphane R. Louboutin1
1 Institut de Mathématiques de Luminy, UPR 9016 163, avenue de Luminy, Case 907 13288 Marseille Cedex 9, France
Colloquium Mathematicum, Tome 96 (2003) no. 2, pp. 207-212.

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

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 $s>0$.
DOI : 10.4064/cm96-2-5
Keywords: prove chi real non principal dirichlet character which chi mathop log nolimits chowlas hypothesis satisfied cannot chowlas method proving chi

Stéphane R. Louboutin 1

1 Institut de Mathématiques de Luminy, UPR 9016 163, avenue de Luminy, Case 907 13288 Marseille Cedex 9, France 
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 $L(s,\chi )$ for $s>0$ and real characters $\chi $
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Stéphane R. Louboutin. Note on a hypothesis implying the
 non-vanishing of Dirichlet $L$-series
 $L(s,\chi )$ for $s>0$ and real characters $\chi $. Colloquium Mathematicum, Tome 96 (2003) no. 2, pp. 207-212. doi : 10.4064/cm96-2-5. http://geodesic.mathdoc.fr/articles/10.4064/cm96-2-5/

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