HYPERGEOMETRIC ZETA FUNCTIONS

Hypergeometric Zeta Functions

This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers. These new properties are treated in detail and are used to d...

Moments of Hypergeometric Hurwitz Zeta Functions

This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called hypergeometric Hurwitz zeta functions, including their analytic continuation to the complex plane and a pre-functional equation satisfied by them. As an application, a formula for moments of hypergeometric H...

A Zero Free Region for Hypergeometric Zeta Functions

This paper investigates the location of ‘trivial’ zeros of some hypergeometric zeta functions. Analogous to Riemann’s zeta function, we demonstrate that they possess a zero free region on a left-half complex plane, except for infinitely many zeros regularly spaced on the negative real axis.

Hypergeometric Functions

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.