# Riemann’s example of a continuous “nondifferentiable” function continued

@article{Segal1978RiemannsEO,
title={Riemann’s example of a continuous “nondifferentiable” function continued},
author={Sanford L. Segal},
journal={The Mathematical Intelligencer},
year={1978},
volume={1},
pages={81-82}
}
• S. Segal
• Published 1 June 1978
• Mathematics
• The Mathematical Intelligencer
18 Citations
On the Mathematical Constitution and Explanation of Physical Facts
. The mathematical nature of modern physics suggests that mathematics is bound to play some role in explaining physical reality. Yet, there is an ongoing controversy about the prospects of
N T ] 2 1 O ct 2 01 7 QUADRATIC RECIPROCITY AND SOME “ NON-DIFFERENTIABLE ” FUNCTIONS
• Mathematics
• 2018
Riemann’s non-differentiable function and Gauss’s quadratic reciprocity law have attracted the attention of many researchers. In [29] Murty and Pacelli gave an instructive proof of the quadratic
Quadratic Reciprocity and Some “Non-differentiable” Functions
• Mathematics
• 2017
Riemann’s non-differentiable function and Gauss’s quadratic reciprocity law have attracted the attention of many researchers. In [28] (Proc Int Conf–Number Theory 1, 107–116, 2004), Murty and Pacelli
Quadratic reciprocity and Riemann’s non-differentiable function
• Mathematics
• 2015
AbstractRiemann’s non-differentiable function and Gauss’s quadratic reciprocity law have attracted the attention of many researchers. Here we provide a combined proof of both the facts. In (Proc.
Arithmetical identities and zeta‐functions
• Mathematics
• 2011
In this paper we establish a class of arithmetical Fourier series as a manifestation of the intermediate modular relation, which is equivalent to the functional equation of the relevant
On some Diophantine fourier series
• Mathematics
• 2010
We continue our study on arithmetical Fourier series by considering two Fourier series which are related to Diophantine analysis. The first one was studied by Hardy and Littlewood in connection with
On riemann “nondifferentiable” function and Schrödinger equation
• Mathematics
• 2010
AbstractThe function  \psi : = \sum\nolimits_{n \in \mathbb{Z}\backslash \left\{ 0 \right\}} {{{e^{\pi i\left( {tn^2 + 2xn} \right)} } \mathord{\left/ {\vphantom {{e^{\pi i\left( {tn^2 + 2xn}
Foundation of Paralogical Nonstandard Analysis and its Application to Some Famous Problems of Trigonometrical and Orthogonal Series
This is an article about foundation of paralogical nonstandard analysis and its applications to the continuous function without a derivative presented by absolutely convergent trigonometrical series
Continuous Nowhere Differentiable Functions
In the early nineteenth century, most mathematicians believed that a continuous function has derivative at a significant set of points. A.~M.~Amp\`ere even tried to give a theoretical justificati ...

## References

SHOWING 1-9 OF 9 REFERENCES
The Differentiability of Riemann's Function
The functiong(x)= :P%-= (sin 7rp2X/7rp2), thought by Riemann to be nowhere differentiable, is shown to be differentiable only at rational points expressible as the ratio of odd integers. The proof
Briefe von K. Weierstrass an Paul du Bois-Reymond
Gosta Mittag-Leffler (1846-1927) publizierte und annotierte in diesem Aufsatz eine Reihe von Briefen uberwiegend mathematischen Inhalts von Karl Weierstras (1815-1897) an den Mathematiker Paul du
THE DIFFERENTIABILITY OF THE RIEMANN FUNCTION AT CERTAIN RATIONAL MULTIPLES OF pi.
• J. Gerver
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1969
It is shown that a continuous function which Riemann is said to have believed to be nowhere differentiable is in fact differentiable at certain points.
Lacunary Taylor and Fourier series
where X is an odd integer à 3, and a a positive number such that a < 1 and aX>l+37r /2 : (2) is a continuous function which is nowhere differentiable [49]. Later on, Weierstrass's result was improved