TITLE:
The Infinite Polynomial Products of the Gamma and Zeta Functions
AUTHORS:
Pál Doroszlai, Horacio Keller
KEYWORDS:
Gamma Function, Zeta Function, Critical Line
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.6,
June
30,
2022
ABSTRACT: Starting with the binomial coefficient and using its infinite product representation, the infinite product representation of the gamma function and of the zeta function are composed of an exponential and of a trigonometric component and proved. It is proved, that all these components define imaginary roots on the critical line, if written in the form as they are in the functional equation of the zeta function.