A general class of Voronoi's and Koshliakov–Ramanujan's summation formulas involvingdk(n)

DOI10.1080/10652469.2010.540447zbMath1235.44007OpenAlexW2134754455MaRDI QIDQ3107305

Semyon B. Yakubovich

Publication date: 23 December 2011

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

Full work available at URL: https://doi.org/10.1080/10652469.2010.540447

zbMATH Keywords

Mellin transformhypergeometric functionsRiemann zeta-functionKontorovich-Lebedev transformDirichlet divisor problemRamanujan's lost notebookVoronoi summation formulaFourier-Watson transformsMellin convolution type transformsmodified Bessel and hyper-Bessel functions

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) 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)

Related Items (5)

New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type ⋮ Explicit transformations of certain Lambert series ⋮ A generalized modified Bessel function and a higher level analogue of the theta transformation formula ⋮ On the curious series related to the elliptic integrals ⋮ A Voronoi-type summation formula involving σ_iτ(n) and index transforms

Cites Work

• On some relations which are equivalent to functional equations involving the Riemann zeta function
• Voronoi–Nasim summation formulas and index transforms
• Koshliakovs Formula and Guinands Formula in Ramanujans Lost Notebook
• ON THE SUMMATION FORMULAE OF VORONOÏ AND POISSON
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