Journal of Integer Sequences, Vol. 15 (2012), Article 12.5.8

Dedekind Sums with Arguments Near Euler's Number e

Kurt Girstmair
Institut für Mathematik
Universität Innsbruck
Technikerstr. 13/7
A-6020 Innsbruck


We study the asymptotic behaviour of the classical Dedekind sums s(m/n) for convergents m/n of e, e2, and (e+1)/(e-1), where e = 2.71828 ... is Euler's number. Our main tool is the Barkan-Hickerson-Knuth formula, which yields a precise description of what happens in all cases.

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Received May 8 2012; revised version received May 31 2012. Published in Journal of Integer Sequences, June 12 2012.

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