We give explicit constants κ such that if χ is a real non-principal Dirichlet character for which L(1,χ) ≤ κ, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that L(s,χ) > 0 for s > 0. These constants are larger than the previous ones κ = 1- log 2 = 0.306... and κ = 0.367... we obtained elsewhere.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-1-8,
author = {S. Louboutin},
title = {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 $\chi$},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {79-90},
zbl = {1334.11069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-1-8}
}
S. Louboutin. On the size of L(1,χ) and S. Chowla's hypothesis implying that L(1,χ) > 0 for s > 0 and for real characters χ. Colloquium Mathematicae, Tome 131 (2013) pp. 79-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-1-8/