Explicit formulas of a generalized Ramanujan sum-Reference-Cited by-同舟云学术

Explicit formulas of a generalized Ramanujan sum

Published:2016-02-18 Issue:02 Volume:12 Page:383-408
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Kühn Patrick¹,Robles Nicolas¹

Affiliation:

1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Abstract

In this paper, explicit formulas involving a generalized Ramanujan sum are derived. An analogue of the prime number theorem is obtained and equivalences of the Riemann hypothesis are shown. Finally, explicit formulas of Bartz are generalized.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042116500238

Reference15 articles.

1. On some complex explicit formulae connected with the Mobius function. I

2. On some complex explicit formulae connected with the Mobius function. II

3. An extension of Ramanujan’s sum

4. Lectures in Advanced Mathematics;Davenport H.,1967

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