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Author(s): Semyon Yakubovich
Title: New summation and transformation formulas of the Poisson, Muntz, Mobius and Voronoi type
Issue Date: 2015
Abstract: Starting from the classical summation formulas and basing on properties of the Mellin transform and Ramanujan's identities, which represent a ratio of products of Riemann's zeta functions of different arguments in terms of the Dirichlet series of arithmetic functions, we obtain a number of new summation formulas of the Poisson, Muntz, Mobius and Voronoi type. The corresponding analogues of the Muntz operators are investigated. Interesting and curious particular cases of summation formulas involving arithmetic functions are exhibited. Necessary and sufficient conditions for the validity of the Riemann hypothesis are derived.
Subject: Matemática
Scientific areas: Ciências exactas e naturais::Matemática
Natural sciences::Mathematics
Document Type: Artigo em Revista Científica Internacional
Rights: openAccess
Appears in Collections:FCUP - Artigo em Revista Científica Internacional

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