New summation and transformation formulas of the Poisson, Muntz, Mobius and Voronoi type

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Semyon Yakubovich (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 26

Pages: 768-795

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 2 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00G-DCY

DOI: 10.1080/10652469.2015.1051483

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 28