Integral and series transformations via Ramanujan's identities and Salem's type equivalences to the Riemann hypothesis

DOI10.1080/10652469.2013.838762zbMath1348.44005arXiv1206.1166OpenAlexW2116692805MaRDI QIDQ5404136

Semyon B. Yakubovich

Publication date: 21 March 2014

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.1166

zbMATH Keywords

Mellin transformmodified Bessel functionsLambert seriesRiemann zeta-functionRiemann hypothesisKontorovich-Lebedev transformMöbius transformarithmetic functionsLambert transformRamanujan's formulas

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) (zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (6)

New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type ⋮ Generalized Lambert-type transforms over integrable Boehmians ⋮ Approaching the Riemann hypothesis using Salem's equivalence and inversion formulae of a Widder–Lambert-type transform ⋮ Inversion formulae for a Lambert-type transform and the Salem's equivalence to the Riemann hypothesis ⋮ On the curious series related to the elliptic integrals ⋮ On Müntz-type formulas related to the Riemann zeta function

Cites Work

• Unnamed Item
• Inversions of generalized Lambert transforms
• Widder's inversion formula for the Lambert transform
• A Class of Index Transforms with General Kernels

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