Fractional Hypergeometric Zeta Functions

Since Riemann, there have been a great number of generalizations of the Riemannrnzeta function. Of particular interest is the hypergeometric zeta functions a generalizationrndue to Hassen and Nguyen that satisfies many of the same properties as thernclassical Riemann zeta function. In this dissertation we show that the second orderrnHypergeometric Zeta Function has zero free region in the right half of the complexrnplane and extend the hypergeometric zeta Functions to fractional hypergeometric zetarnfunctions. We rewrite the series representation of the second order hypergeometricrnzeta function as a ”power series” with Dirichlet series as its coefficients. We use thisrnseries representation to show that the second order hypergeometric zeta function hasrnzero free region to the right half of the complex plane. We generalize the hypergeometricrnzeta function via the integral representation of the classical Riemann zetarnfunction to fractional hypergeometric zeta functions. It is shown that fractional hypergeomericrnzeta functions satisfy many of the properties satisfied by hypergeometricrnzeta functions

Get Full Work

Report copyright infringement or plagiarism