A version of Carleman’s formula summation of the Riemann $\zeta$-function on the critical line

Author A. M. Brydun, P. A. Yatsulka
a_brydun@yahoo.com, petroandr@rambler.ru
Lviv Polytechnic National University, Lviv National University

Abstract A version of Carleman's formula for functions holomorphic in a rectangle is proved. It is applied to the evaluation of the integral of $\zeta$-function logarithm with the summing factor $\exp(-t)$ along the critical line. This allowed to obtain a new statement equivalent to the Riemann hypothesis.
Keywords $\zeta$-function; Carleman's formula
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Pages 3-8
Volume 35
Issue 1
Year 2011
Journal Matematychni Studii
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