On some relations for Mellin transforms of Hardy's function

Aleksandar Ivić

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arXiv · 1012.3836

On some relations for Mellin transforms of Hardy's function

Aleksandar Ivić

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Abstract

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

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Aleksandar Ivić. 2010-12-17. On some relations for Mellin transforms of Hardy's function. https://arxiv.org/abs/1012.3836

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