General Mathematics


The Domain of the Riemann Zeta Function on the Complex Plane

Authors: Armando M. Evangelista Jr.

The Riemann zeta-function is one of the most studied complex function in mathematics. Riemann in his 1859 paper On the Number of Prime Numbers less than a Given Quantity [1] claimed that the analytic continuation of the zeta-function extends its domain over the entire complex plane except at s = 1. But, as I’ve shown in my two papers: A Short Disproof of the Riemann Hypothesis [2] and Riemann’s Functional Equation is Not Valid and Its Implication on the Riemann Hypothesis [3], the zeta-function is only defined on the right half-plane. It is the purpose of this present work to precisely locate the domain of this function on the right half-plane.

Comments: 4 Pages.

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Submission history

[v1] 2018-08-31 10:12:33
[v2] 2018-09-01 16:01:06
[v3] 2018-10-26 22:40:20

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