Remarks on `Riemann's example' \(\sum_{n=1}^ \infty {\sin n^ 2x\over n^ 2}\) of a continuous, non-differentiable function
type: Item
instance of: scholarly article
title: Remarks on `Riemann's example' \(\sum_{n=1}^ \infty {\sin n^ 2x\over n^ 2}\) of a continuous, non-differentiable function
zbMATH Open document ID: 0874.01003
DOI: 10.1007/BF03322163
author: Peter Ullrich
published in: Results in Mathematics
publication date: 1997-11-11T00:00:00Z
review text: According to Weierstraß Riemann had claimed in his lectures of 1861 that this function was non-differentiable on a dense point set. New sources confirm that both Weierstraß and Kronecker gave proofs, and back up the Riemannian origin of the function. Also, the author gives a proof in the style of Riemann, using information on the growth of the theta series at the boundary of its domain of convergence, as found in a fragment by Riemann.
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 26A27
Mathematics Subject Classification ID: 26-03
zbMATH DE Number: 1029202
zbMATH Keywords: non-differentiability
zbMATH Keywords: theta series
zbMATH Keywords: Riemann
zbMATH Keywords: Kronecker
zbMATH Keywords: Weierstraß
reviewed by: Detlef Laugwitz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1029202