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
View on Springer
18 Citations
Background Citations
1
Methods Citations
1

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
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
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
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
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…
Sources in the Development of Mathematics: Index
On some Diophantine fourier series
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
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 ...
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References

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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…
Riemann’s example of a continuous, ’nondifferentiable’ function
Weierstrass’s non-differentiable function
ON SOME INFINITE SERIES INVOLVING ARITHMETICAL FUNCTIONS (II)
The Differentiability of the Riemann Function at Certain Rational Multiples of π
More on the Differentiability of the Riemann Function
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…