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

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Semyon Yakubovich (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 25

Pages: 255-271

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 7 Citations

Other information

Authenticus ID: P-009-5YT

DOI: 10.1080/10652469.2013.838762

Abstract (EN): We consider integral and series transformations, which are associated with Ramanujan's identities, involving arithmetic functions a(n), (n), sigma(a)(n), d(n), (n), (n), phi(n) and a ratio of products of Riemann's zeta functions of different arguments. Reciprocal inversion formulas are proved in a Banach space of functions whose Mellin's transforms are integrable over the vertical line Re s>1. Examples of new transformations like Widder-Lambert and Kontorovich-Lebedev type are exhibited. Particular cases include familiar Lambert and Mobius transformations. Finally, a class of equivalences of the Salem type to the Riemann hypothesis is established.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17