English

Zeta Functional Analysis

General Mathematics 2014-11-13 v1

Abstract

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of ζ(2n+1)\zeta(2n+1) in terms of zeta at other fractional points. This paper also establishes and presents new expository notes and perspectives on zeta function theory and functional analysis. In addition, a new fundamental result, in form of a new function called omega Ω(s)\Omega(s), is introduced to analytic number theory for the first time. This new function together with some of its most fundamental properties and other related identities are here disclosed and presented as a new approach to the analysis of sums of generalised harmonic series, related alternating series and polygamma functions associated with Riemann zeta function.

Keywords

Cite

@article{arxiv.1411.3244,
  title  = {Zeta Functional Analysis},
  author = {Michael A. Idowu},
  journal= {arXiv preprint arXiv:1411.3244},
  year   = {2014}
}
R2 v1 2026-06-22T06:56:27.984Z