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KIAM Preprint № 69, Moscow, 2008
Authors: Pustyl'nikov L. D., Lokot T.V.
New results on the Dirichlet L-functions
Abstract:
New theoretical and numerical investigations of the following two problems associated with the Dirichlet L-functions L(s; χ) are carried out in this work: the conjecture on the values L(1/2; χ) and the Extended Riemann Hypothesis for the function L(s; χ) with a character χ = χ(n) being equal to a Legendre symbol (n/p), where p is a prime. New rigorous theoretical results give necessary and sufficient conditions for the validity or refutation of the second conjecture. Numerical investigations performed with a computer for all p < 500000 confirm the necessary condition and do not confirm conditions sufficient to its refutation. An analytic approximation of the numerical distribution is found as well.
Publication language: russian,  pages: 10
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Pustyl'nikov L. D.,  KIAM RAS
  • Lokot T.V.