An Elementary Problem Equivalent to the Riemann Hypothesis

2000/08/31 by Jeffrey C. Lagarias · 3 citations
Mathematics · #math.NT #msc:11M26 #msc:11A25

paper · pdf

published as Amer. Math. Monthly 109 (2002), 534--543 · 9 pages, Latex, explanatory section 2 added; proofs simplified

arxiv created 2001/05/06 · arxiv updated 2009/11/30

Abstract

This paper shows the equivalence of the Riemann hypothesis to an sequence of elementary inequalities involving the harmonic numbers H_n, the sum of the reciprocals of the integers from 1 to n. It is a modification of a criterion due to Guy Robin.

Cited by

• On the Least Colossally Abundant Exception to Robin's Inequality
• Off Critical Zeros Contradict Contraction in the Dynamical Reformulation of the Riemann Hypothesis
• A Dynamical Criterion Equivalent to the Riemann Hypothesis

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