Note on a hypothesis implying the non-vanishing of Dirichlet L-series L(s,χ) for s > 0 and real characters χ Stéphane R. Louboutin (2003) Colloquium Mathematicae We prove that if χ is a real non-principal Dirichlet character for which L(1,χ) ≤ 1- log2, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that L(s,χ) > 0 for s > 0.
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