On the zeros of Dirichlet L-functions. IV.
Akio Fujii (1976)
Journal für die reine und angewandte Mathematik
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Akio Fujii (1976)
Journal für die reine und angewandte Mathematik
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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.
Matti Jutila (1975-1976)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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J.B. Conrey, A. Ghosh (1988)
Inventiones mathematicae
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H.S. Shapiro, A.L. Shields (1962/63)
Mathematische Zeitschrift
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K. Ramachandra, A. Sankaranarayanan (1994)
Mathematica Scandinavica
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Wenpeng Zhang, Weili Yao (2004)
Acta Arithmetica
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Bruce Berndt (1975)
Acta Arithmetica
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Enrico Bombieri, Alberto Perelli (2001)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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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.
Frieder Grupp (1988)
Acta Arithmetica
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Lennart Carleson (1952)
Mathematische Zeitschrift
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