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

S. Louboutin

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Displaying similar documents to “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”

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

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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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Bruce Berndt (1975)

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Explicit upper bounds for |L(1,χ)| for primitive even Dirichlet characters

Stéphane Louboutin (2002)

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Some problems concerning roots of polynomials with Dirichlet characters as coefficients

J. Kaczorowski (1985)

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Explicit upper bounds for |L(1,χ)| when χ(3) = 0

David J. Platt, Sumaia Saad Eddin (2013)

Colloquium Mathematicae

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Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.