Exploring zero free regions for fractional hypergeometric zeta functions.

In this paper the product of classical Riemann zeta function ζ (s) and fractional hypergeometric zeta functions ζ a (s) is examined. As a result of this product a new integral representation of the square of the Riemann zeta function is obtained. We use this integral representation to show that some special Mellin transforms which are naturally related to the fractional hypergeometric zeta functions have zero free regions in the specified right half of the complex plane. Finally we show that the fractional hypergeometric zeta functions ζ a (s) are zero free for some specified values of a. [ABSTRACT FROM AUTHOR]