On some relations for Mellin transforms of Hardy's function

Abstract

Some relations involving the Mellin and Laplace transforms of powers of the classical Hardy function $$Z(t):=\zeta (1/2+it)(\chi (1/2+it){)}^{-1/2},\zeta (s)=\chi (s)\zeta (1-s)$$ are obtained. In particular, we discuss some mean square identities and their consequences.

18 pages

References in corpus (3)

• On some reasons for doubting the Riemann hypothesis
• The Laplace transform of the fourth moment of the zeta-function
• Zeros of the Riemann zeta function on the critical line