Preprint
Hypothesis

On the Riemann-Hardy Conjecture for the Ramanujan Zeta-Function

Altmetrics

Downloads

363

Views

280

Comments

0

This version is not peer-reviewed

Submitted:

29 May 2021

Posted:

31 May 2021

You are already at the latest version

Alerts
Abstract
In this article we propose the integral, series and product representations for the Ramanujan zeta-function. We suggest a variant for the Conrey-Ghosh product for the entire Ramanujan zeta-function. We present some variants for the product for the Ramanujan $\Xi$-function. We prove that all of its zeros are real. Along the way we obtain the truth of the Riemann-Hardy conjecture.
Keywords: 
Subject: Computer Science and Mathematics  -   Algebra and Number Theory
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
Prerpints.org logo

Preprints.org is a free preprint server supported by MDPI in Basel, Switzerland.

Subscribe

© 2024 MDPI (Basel, Switzerland) unless otherwise stated