On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis

  • S. Beltraminelli CERFIM, Research Center Math. and Phys., Locarno, Switzerland
  • D. Merlini CERFIM, Research Center Math. and Phys., Locarno, Switzerland
  • S. K. Sekatskii LPMV, Ecole Polytechnique F´ed´erale de Lausanne, Switzerland

Abstract

Using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytical function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and present some of them as an example. It is shown that all earlier known equalities of this type, viz., the Wang equality, Volchkov equality, Balazard-Saias-Yor equality, and an equality established by one of the authors, are certain particular cases of our general approach.
Published
25.02.2012
How to Cite
BeltraminelliS., MerliniD., and SekatskiiS. K. “On Equalities Involving Integrals of the Logarithm of the Riemann ζ-Function and Equivalent to the Riemann Hypothesis”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 2, Feb. 2012, pp. 218-2, http://umj.imath.kiev.ua/index.php/umj/article/view/2568.
Section
Research articles