Dedekind Sums with Arguments Near Euler's Number e
Kurt Girstmair
Institut für Mathematik
Universität Innsbruck
Technikerstr. 13/7
A-6020 Innsbruck
Austria
Abstract:
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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