Ramanujan's theorem and highest abundant numbers

Autor:	Musin, Oleg R.
Rok vydání:	2019
Předmět:	Mathematics - Number Theory Mathematics - Combinatorics
Zdroj:	Arnold Mathematical Journal; Vol 6:1 (2020); 119-130
Druh dokumentu:	Working Paper
DOI:	10.1007/s40598-020-00136-w
Popis:	In 1915, Ramanujan proved asymptotic inequalities for the sum of divisors function, assuming the Riemann hypothesis (RH). We consider a strong version of Ramanujan's theorem and define highest abundant numbers that are extreme with respect to the Ramanujan and Robin inequalities. Properties of these numbers are very different depending on whether the RH is true or false. Comment: 12 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.09327 Zobrazit plný text záznamu View this record from Arxiv