Dedekind sums with arguments near certain transcendental numbers

2013/04/11 by Kurt Girstmair, Girstmair, Kurt
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1304.3319

9 pages

arxiv created 2013/04/11 · openalex publication_date 2013/04/11 · arxiv updated 2013/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of the classical Dedekind sums s(s_k/t_k) for the sequence of convergents s_k/t_k k≥ 0, of the transcendental number \BD ∑_j=0^∞\frac 1b^2j, b≥ 3. \ED In particular, we show that there are infinitely many open intervals of constant length such that the sequence s(s_k/t_k) has infinitely many transcendental cluster points in each interval.

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