New Zero-Free Regions for Hypergeometric Zeta and Fractional Hypergeometric Zeta Functions - Demessie Ergabus Birmechu; Hunduma Legesse Geleta (Journal of Mathematics)
We describe and demonstrate zero-free regions for the families called “hypergeometric zeta functions” and “fractional hypergeometric zeta functions”. These zero-free regions are vertical strips in the right half of the complex plane. In the proofs, we utilize positivity results on the oscillatory integrals and monotonicity of real-valued functions to demonstrate these zero-free regions for both families.