On some relations for Mellin transforms of Hardy's function

Details On some relations for Mellin transforms of Hardy's function On some relations for Mellin transforms of Hardy's function

2010-12-17

arxiv.org/abs/1012.3836v1

Mathematics

Number Theory

18 pages

Scientific paper

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

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