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2006 Abundant Numbers and the Riemann Hypothesis
Keith Briggs
Experiment. Math. 15(2): 251-256 (2006).

Abstract

In this note I describe a computational study of the successive maxima of the relative sum-of-divisors function $\rho(n):=\sigma(n)/n$. These maxima occur at superabundant and colossally abundant numbers, and I also study the density of these numbers. The values are compared with the known maximal order $e^\gamma\loglog{n}$; theorems of Robin and Lagarias relate these data to a condition equivalent to the Riemann Hypothesis. It is thus interesting to see how close these conditions come to being violated.

Citation

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Keith Briggs. "Abundant Numbers and the Riemann Hypothesis." Experiment. Math. 15 (2) 251 - 256, 2006.

Information

Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1149.11041
MathSciNet: MR2253548

Subjects:
Primary: 11M26 , 11N64 , 11Y55

Keywords: abundant numbers , Riemann hypothesis

Rights: Copyright © 2006 A K Peters, Ltd.

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Vol.15 • No. 2 • 2006
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