Über trigonometrische Reihen mit zahlentheoretischen Koeffizienten. (On some trigonometric series with number theoretic coefficients)
type: Item
instance of: scholarly article
title: Über trigonometrische Reihen mit zahlentheoretischen Koeffizienten. (On some trigonometric series with number theoretic coefficients)
zbMATH Open document ID: 0727.11030
DOI: 10.1007/BF01199062
author: Dieter Wolke
author: Lutz G. Lucht
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: The authors study the series \(T(\alpha)=\sum_{p prime}\frac{\sin (2\pi p\alpha)}{p}\). It is shown that it is uniformly convergent for \(\alpha\in {\mathbb{R}}\). The function T is nondifferentiable on a noncountable set of measure zero and nowhere of bounded variation. It is highly probable that T is nowhere differentiable, but this seems to be a hard problem. In the proofs estimates for exponential sums with primes (Vinogradov's bound) and the theorem of Siegel-Walfisz are used. The main ideas are similar to those introduced by the authors in two earlier papers [Math. Z. 149, 155- 167 (1976; Zbl 0312.10026); Acta Math. Acad. Sci. Hung. 33, 263-288 (1979; Zbl 0419.10036)].
Mathematics Subject Classification ID: 11L40
Mathematics Subject Classification ID: 11L20
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 4200304
zbMATH Keywords: trigonometric series
zbMATH Keywords: nondifferentiability
zbMATH Keywords: estimates for exponential sums
zbMATH Keywords: theorem of Siegel-Walfisz
reviewed by: Lutz G. Lucht
MaRDI profile type: Publication
cites work: The Differentiability of the Riemann Function at Certain Rational Multiples of &#960
cites work: Trigonometrische Reihen Über Multiplikativen Zahlenmengen. II
cites work: Exponential sums with multiplicative coefficients
cites work: Q3731703
cites work: The Differentiability of Riemann's Function
description: scientific article; zbMATH DE number 4200304