Dedekind sums in the $p$-adic number field

Kurt Girstmair

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arXiv · 1609.03162

Dedekind sums in the $p$-adic number field

Kurt Girstmair

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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 $\mathbb Z_2$ or $\mathbb Z_3$, so they are not dense in $\mathbb Q_2$ or $\mathbb Q_3$. But they are dense in $\mathbb Q_p$ if $p\ge 5$.

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BibTeX RIS

Kurt Girstmair. 2016-09-11. Dedekind sums in the $p$-adic number field. https://arxiv.org/abs/1609.03162

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