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New Zero-Free Regions for Hypergeometric Zeta and Fractional Hypergeometric Zeta Functions

Author

Listed:
  • Demessie Ergabus Birmechu
  • Hunduma Legesse Geleta
  • Serkan Araci

Abstract

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.

Suggested Citation

  • Demessie Ergabus Birmechu & Hunduma Legesse Geleta & Serkan Araci, 2022. "New Zero-Free Regions for Hypergeometric Zeta and Fractional Hypergeometric Zeta Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-5, May.
    • Handle: RePEc:hin:jjmath:4862447
    DOI: 10.1155/2022/4862447
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