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Subjects
11-XX Number theory
11Mxx Zeta and $L$ -functions: analytic theory
11M20 Real zeros of $L (s, χ)$ ; results on $L (1, χ)$

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Nonvanishing of quadratic Dirichlet $L$ -functions at $s = \frac{1}{2}$ .

Soundararajan, K. (2000)

Annals of Mathematics. Second Series

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.

Currently displaying 1 – 2 of 2

Page 1

Displaying 1 – 2 of 2

Nonvanishing of quadratic Dirichlet L -functions at s = 1 2 .

Note on a hypothesis implying the non-vanishing of Dirichlet L-series L(s,χ) for s > 0 and real characters χ

Currently displaying 1 – 2 of 2

Nonvanishing of quadratic Dirichlet $L$ -functions at $s = \frac{1}{2}$ .