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KIAM Preprint № 54, Moscow, 2010
Authors: Pustyl'nikov L. D.
A new necessary condition for the validity of the Riemann hypothesis
It is obtained results related to the Riemann function ξ(s) which give a new necessary condition for the validity of Riemann hypothesis on the zeros of the classical zeta-function. It is proved that if at least one even derivative of the function ξ(s) at the point s = 1/2 is not positive, then the Riemann hypothesis would be false. However, it is also proved that all the even derivatives at the point s = 1/2 are strictly positive and their asymptotic form for the order of derivatives tending to ininity is found.
Publication language: russian,  pages: 8
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Pustyl'nikov L. D.,  KIAM RAS