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A Variant of the Fractional Gamma-regularized Zeta Kernel
Hunduma Legesse Geleta
In this paper, we introduce and study a special function, referred to as a variant of the fractional gamma-regularized zeta kernel, in which the lower incomplete gamma function app…
Automorphic Integrals with Rational Period Functions and Arithmetical Identities
Tewlede G/Egziabher, Hunduma Legesse Geleta, Abdul Hassen
In 1961, Chandrasekharan and Narasimhan showed that for a large class of Dirichlet series the functional equation and two types of arithmetical identities are equivalent. In 1992,…
More Zero-Free Regions for Fractional Hypergeometric Zeta Functions
Demessie Ergabus Birmechu, Hunduma Legesse Geleta
Some zero-free regions were known on the right half of the complex plane in the form of vertical strips for fractional hypergeometric zeta functions. In this paper, we describe and…
Automorphic Integrals with Log-polynomial Period Functions and Arithmetical Identities
Tewlede G/Egziabher, Hunduma Legesse Geleta, Abdul Hassen
Building on the works of S. Bochner on equivalence of modular relation with functional equation associated to the Dirichlet series, K. Chandrasekharan and R. Narasimhan obtained ne…