Disproving the Euler Product equal to the Riemann Zeta Function

08 August 2024, Version 3
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

The author of this article has already disproved the Euler product equal to the Riemann zeta function that the earlier mathematicians proved. This article presents the main reason why the Euler product is not equal to the Riemann zeta function.

Keywords

computation
infinite product
zeta function

Comments

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Comment number 2, Saleh Omran: Aug 19, 2024, 18:49

The Proof incorrect. 1- \zeta(1) is equal the harmonic series it should be divergence , so the product in equation (4 ) never be greater than \zeta(1). Also the product is diverge slowly to infinity and likewise \zeta(1) diverge very slowly. 2- Again the product in equation 3 line below grow approximately to the value 1.644934 and not exceed the value of \zeta(2). So there is no contradiction and the product is not greater than \zeta(2). And So on...

Comment number 1, Chinnaraji Annamalai: Aug 12, 2024, 07:59

Under the subdivision "4. The Main Reason why the Euler Product is not equal to the Riemann Zeta Function": 1 to the power of any number is 1. For comparison on s =2, we must do the following without loss of generality: 1 to ∞ {(∑xi)-1} < {(∑yi)-1}.