Dedekind sums in the p-adic number field

2016/09/11 by Girstmair, Kurt
#11F20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.03162

Abstract

In a recent note W. Kohnen asks whether the values of Dedekind sums are dense in the field of p-adic numbers. The present paper answers this question. Dedekind sums do not approximate units of \mathbb Z₂ or \mathbb Z₃, so they are not dense in \mathbb Q₂ or \mathbb Q₃. But they are dense in \mathbb Q_p if p≥ 5.

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• Mean values of Dedekind sums
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