On the zeros of Dirichlet L-functions. IV.
Akio Fujii (1976)
Journal für die reine und angewandte Mathematik
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Displaying similar documents to “Distribution of zeros of Dirichlet L-functions and an explicit formula for ψ(t,χ)”
On the zeros of Dirichlet L-functions. IV.
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Under certain mild analytic assumptions one obtains a lower bound, essentially of order , for the number of zeros and poles of a Dirichlet series in a disk of radius . A more precise result is also obtained under more restrictive assumptions but still applying to a large class of Dirichlet series.
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2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15. We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent...
Note on a hypothesis implying the non-vanishing of Dirichlet L-series L(s,χ) for s > 0 and real characters χ
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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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