10.46298/hrj.2022.7663
https://hrj.episciences.org/7663
Mehta, Jay
Jay
Mehta
Zhu, P. -Y
P. -Y
Zhu
Proof of the functional equation for the Riemann zeta-function
In this article, we shall prove a result which enables us to transfer from finite to infinite Euler products. As an example, we give two new proofs of the infinite product for the sine function depending on certain decompositions. We shall then prove some equivalent expressions for the functional equation, i.e. the partial fraction expansion and the integral expression involving the generating function for Bernoulli numbers. The equivalence of the infinite product for the sine functions and the partial fraction expansion for the hyperbolic cotangent function leads to a new proof of the functional equation for the Riemann zeta function.
episciences.org
[MATH]Mathematics [math]
2022-01-09
2022-01-09
2022-01-09
en
journal article
https://hal.archives-ouvertes.fr/hal-03251104v2
2804-7370
https://hrj.episciences.org/7663/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021
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