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

  • S. L. Segal
Dialogue

References

  1. [1]
    Davenport, H., On some infinite series involving arithmetic functions, Quarterly Journal of Mathematics 8 (1937), pp. 8–13 and part II, same volume, pp. 313–320.CrossRefGoogle Scholar
  2. [2]
    Garg, K. M., Mathematical Reviews, vol. 46 (1937) Review No.7451 (p. 1286, Review of [9] ).Google Scholar
  3. [3]
    Gerver, J., The Differentiability of the Riemann Fuction at Certain Rational Multiples of π, Proc. Nat. Acad. Sci. 62, (1969), pp. 668–670.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Gerver, J., The Differentiability of the Riemann Function at Certain Rational Multiples of π, Amer. J. Math 92, (1970), pp. 33–55.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Gerver, J., More on the Differentiability of the Riemann Funktion at Certain Rational Multiples of π, Amer. J. of Math. 93 (1971), pp. 33–41.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Hardy, G. H., Weierstrass’s Non-Differentiable Function, Transactions Am. Math. Soc. 17, (1916), pp. 301–325.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Kahane, J. P., Lacunary Taylor and Fourier Series, Bull. Am. Math. Soc. 70, (1964), pp. 199–213.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Neuenschwander, E., Riemann’s Example of a Continuous, “Nondifferentiable” Function, The Mathematical Intelligencer 1, (1978), pp. 40–44.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Smith, A., The Differentiability of Riemann’s Function, Proc. Am. Math. Soc. 34 (1972), pp. 463–468.MATHCrossRefGoogle Scholar
  10. [10]
    Weierstrass, K., Letter of 23 November 1873 to Paul DuBois-Reymond, reprinted in Acta Mathematica, 39, (1923), pp. 199–201.MATHCrossRefGoogle Scholar
  11. [11]
    Weierstrass, K., über continuirliche Functionen eines Reellen Arguments, die für keinen Werth des letzteren einen bestimmten Differentialquotienten besitzen, K. Weierstrass, Mathematische Werke II, pp. 71–74 (paper read in the Academy of Sciences 18 July (1872).Google Scholar
  12. [12]
    Weierstrass, K., Letter of 10 February 1876 to L. Koenigsberger reprinted in Acta Mathematica 39 (1923), pp. 231–234.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 1978

Authors and Affiliations

  • S. L. Segal
    • 1
  1. 1.University of Rochester RochesterNew YorkUSA

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