Number Theory

    

Complex Extensions of Riemann Zeta Function and Complementary Formula of Gama Function

Authors: Xiaochun Mei

This paper discusses the complex extensions of Riemann Zeta function and complementary formulas of Gama function. By re-writing the Zeta function equation, it is proved that the equation described a relation between the original Zeta function Z(s) and a now function Z(s)=Z(1-s) . But the domains of these two function does not the same and incompatible, so the Riemann Zeta function equation does not hold. It is also proved that the complex extension formula of the present complementary formula of Gama function is wrong. The correct formula is given by strict calculation. The condition 01. Therefore, Riemann Zeta function equation does not hold at any point in the complex plane, and it is meaningless to discuss it.

Comments: 13 Pages.

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Submission history

[v1] 2025-03-05 21:21:05

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