Delicacy of the Riemann hypothesis and certain subsequences of superabundant numbers

2013/06/13 by Sadegh Nazardonyavi, Semyon Yakubovich, Nazardonyavi, Sadegh +1
Mathematics · #11-XX #97Fxx #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11-XX #msc:97Fxx

paper · pdf · doi:10.48550/arxiv.1306.3434

one lemma is omitted, and some inequalities clarified

arxiv created 2013/06/17 · arxiv updated 2013/06/18

Abstract

Robin's theorem is one of the ingenious reformulation of the Riemann hypothesis (RH). It states that the RH is true if and only if σ(n)<e^γnloglog n for all n>5040 where σ(n) is the sum of divisors of n and γ is Euler's constant. In this paper we show that how the RH is delicate in terms of certain subsets of superabundant numbers, namely extremely abundant numbers and some of its specific supersets.

Related

• Superabundant numbers, their subsequences and the Riemann hypothesis
• On the Least Colossally Abundant Exception to Robin's Inequality
• A family of analogues to the Robin criterion
• A New Type of Abundant Numbers
• Riemann hypothesis equivalences, Robin inequality, Lagarias criterion, and Riemann hypothesis