The Laplace and Mellin transforms of powers of the Riemann zeta-function

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dc.creatorIvić, Aleksandar
dc.date2006-05-29
dc.date2006-06-02
dc.date.accessioned2026-07-07T07:14:36Z
dc.date.available2026-07-07T07:14:36Z
dc.descriptionThis paper gives a survey of known results concerning the Laplace transform $$ L_k(s) := \int_0^\infty |ζ(1/2+ ix)|^{2k}{\rm e}^{-sx}{\rm d} x \qquad(k \in N, \R s > 0), $$ and the (modified) Mellin transform $$ {\cal Z}_k(s) := \int_1^\infty|ζ(1/2+ ix)|^{2k}x^{-s}{\rm d} x\qquad(k\in N), $$ where the integral is absolutely convergent for $\R s \ge c(k) > 1$. Also some new results on these integral transforms of $|ζ(1/2+ ix)|^{2k}$ are given, which have important connections with power moments of the Riemann zeta-function $ζ(s)$.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0605721
dc.identifierhttp://arxiv.org/abs/math/0605721
dc.identifierInternational J. of Mathematics and Analysis Vol. 1 No. 2, 2006, pp. 131-140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112939
dc.subjectNumber Theory
dc.subject11M06, 11F72
dc.titleThe Laplace and Mellin transforms of powers of the Riemann zeta-function
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