On Robin’s criterion for the Riemann hypothesis
YoungJu Choie, Nicolas Lichiardopol, Pieter Moree, Patrick Solé (2007)
Journal de Théorie des Nombres de Bordeaux
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Robin’s criterion states that the Riemann Hypothesis (RH) is true if and only if Robin’s inequality is satisfied for , where denotes the Euler(-Mascheroni) constant. We show by elementary methods that if does not satisfy Robin’s criterion it must be even and is neither squarefree nor squarefull. Using a bound of Rosser and Schoenfeld we show, moreover, that must be divisible by a fifth power . As consequence we obtain that RH holds true iff every natural number divisible by...