New Results for Sorli's Conjecture on Odd Perfect Numbers - Part II

2013/03/10 by Jose Arnaldo B. Dris, Dris, Jose Arnaldo B. · 1 citation
Mathematics · #11A05 (Primary) 11J25 #11J99 (Secondary) #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1303.2329

openalex publication_date 2013/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If N=q^kn² is an odd perfect number given in Eulerian form, then Sorli's conjecture predicts that k=ν_q(N)=1. In this article, we give some further results related to this conjecture and those contained in the papers \citeDris and \citeDris2. (withdrawn because of a crucial gap in Theorem 1 [see https://arxiv.org/pdf/1309.0906.pdf for what is currently provable in this regard], as well as elementary mistakes in the numerical bounds from pages 2 to 4)

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