Congruences mod 4 for the alternating sum of the partial quotients

2015/01/04 by Kurt Girstmair, Girstmair, Kurt · 1 citation
Mathematics · #11A55 #11F20 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11A55 #msc:11F20

paper · pdf · doi:10.48550/arxiv.1501.00655

openalex publication_date 2015/01/04 · arxiv created 2015/01/07 · arxiv updated 2015/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply a technique used in [Tsukerman, Equality of Dedekind sums mod \mathbb Z, 2\mathbb Z and 4\mathbb Z, arXiv:1408.3225] combined with the Barkan-Hickerson-Knuth-formula in order to obtain congruences mod 4 for the alternating sum of the partial quotients of the continued fraction expansion of a/b, where 0<a<b are integers.

Citations

• Equality of Dedekind sums mod ℤ,2ℤ and 4ℤ

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• Equality of Dedekind sums mod 8 ℤ

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