Note on the Odd Perfect Numbers

EasyChair Preprint 8121, version 7

Abstract

The Riemann Hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. Under the assumption of the Riemann Hypothesis, we prove that there is not any odd perfect number at all.

Keyphrases: Odd perfect numbers, Riemann hypothesis, Superabundant numbers, prime numbers, sum-of-divisors function

@booklet{EasyChair:8121,
  author    = {Frank Vega},
  title     = {Note on the Odd Perfect Numbers},
  howpublished = {EasyChair Preprint 8121},
  year      = {EasyChair, 2022}}