Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 13 (2018), 251 -- 263

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ON THE DISTRIBUTION OF DEDEKIND SUMS

Kurt Girstmair

Abstract. Dedekind sums have applications in quite a number of fields of mathematics. Therefore, their distribution has found considerable interest. This article gives a survey of several aspects of the distribution of these sums. In particular, it highlights results about the values of Dedekind sums, their density and uniform distribution. Further topics include mean values, large and small (absolute) values, and the behaviour of Dedekind sums near quadratic irrationals. The present paper can be considered as a supplement to the survey article [9].

2010 Mathematics Subject Classification: 11R20.
Keywords: Dedekind sums; distribution of Dedekind sums.

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Kurt Girstmair
Institut für Mathematik,
Universität Innsbruck,
Technikerstr. 13/7
A-6020 Innsbruck, Austria.
e-mail: Kurt.Girstmair@uibk.ac.at

http://www.utgjiu.ro/math/sma