On some relations for Mellins transforms of Hardy's function

zbMATH Open1270.11083arXiv1012.3836MaRDI QIDQ2910115

Aleksandar Ivić

Publication date: 7 September 2012

Published in: Commentarii Mathematici Universitatis Sancti Pauli (Search for Journal in Brave)

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

Full work available at URL: https://arxiv.org/abs/1012.3836

zbMATH Keywords

momentsMellin transformRiemann zeta-functionHardy Z-function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (3)

On the Mellin transforms of powers of Hardy's function ⋮ THE MELLIN TRANSFORM OF THE SQUARE OF RIEMANN'S ZETA-FUNCTION ⋮ On some conjectures and results for the Riemann zeta-function and Hecke series

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