%0 Journal Article
%T New summation and transformation formulas of the Poisson, M¨¹ntz, M£¿bius and Voronoi type
%A Semyon Yakubovich
%J Mathematics
%D 2014
%I arXiv
%X 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 the Poisson, M\"{u}ntz, M\"{o}bius and Voronoi type summation formulas. The corresponding analogs of the M\"{u}ntz 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.
%U http://arxiv.org/abs/1410.7934v3