Number Theory

    

A New Formula for the Riemann Hypothesis

Authors: Ciro Cesarano

By a simple extension of rearrangement definition of a simply converging series, at non standard model of analysis, the author finds a new formula for ζ* (s) with s C*complex hyperreal numbers set with a *> 0 and with s ≠1 .However this new formula is very easily extendable at the whole complex plane with s ≠1 . Notable result is that with the definition of " non standard rearrangement " the commutative property of addition continues to hold even for simply convergent series (such as harmonic series with alternate signs). Moreover the author, by means of the new formula of ζ*(s) and the corresponding functional equation, gives a proof of the Riemann hypothesis.

Comments: 17 Pages.

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Submission history

[v1] 2024-09-24 01:44:33
[v2] 2025-05-05 18:54:43
[v3] 2026-04-21 17:57:13

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