Riemann Hypothesis may be proved by induction

TL;DR

This paper proposes a novel approach using sum identities and induction to potentially prove the Riemann Hypothesis and introduces a new series for Euler's constant gamma.

Contribution

It introduces new sum identities related to harmonic numbers and suggests a method to prove the Riemann Hypothesis by induction, also deriving a new series for gamma.

Findings

Derived new identities for harmonic and oscillatory numbers

Proposed a possible proof of the Riemann Hypothesis via induction

Discovered a new series representation for Euler's constant gamma

Abstract

The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At least one of these identities may be applied to prove the Riemann Hypothesis by induction. Additionally using this approach, the new series for Euler's constant gamma has been found.