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KIAM Preprint № 69, Moscow, 2006
Authors: Pustyl'nikov L. D.
Some properties of Dirichlet L-functions associated with their nontrivial zeros
Abstract:
The connection between the values of the L-functions at the point s=1/2 and Gauss sums which leads to the sufficient condition for the validity of the equality L(1/2,χ)=0 is studied. The necessary conditions for the validity of the Extended Riemann Hypothesis for the L-fuctions are given in terms of the signs of the even-order derivatives of the fuctionn ξ(s,χ) which is an analogue of the Riemann ξ-function ξ(s). All the results are applied to the L-functions L(s,χ)$ with a character χ being equal to a Legendre symbol.
Publication language: russian
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Pustyl'nikov L. D.,  KIAM RAS