A pencil of K3- surfaces related to Apéry's recurrence for ζ(3) and Fermi surfaces for potential zero

  • C. Peters
  • J. Steinstra
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1399)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Be]
    F. Beukers: Another congruence for the Apéry numbers, Journ. of Number Theory, 25, 1987, 201–210.MathSciNetCrossRefMATHGoogle Scholar
  2. [Be2]
    F. Beukers: Irrationality proofs using modular forms. Journées Arithm. Besançon (1985), Astérisque, 147, 1987, 271–283, 345.MathSciNetMATHGoogle Scholar
  3. [B-P]
    F. Beukers, C. Peters: A family of K3-surfaces and ζ(3), Journ. f. reine u. angew. Math., 351, 1984, 42–54.MathSciNetMATHGoogle Scholar
  4. [G-K-T]
    D. Gieseker, H. Knörrer, E. Trubowitz: Fermi curves and density of states, forthcoming.Google Scholar
  5. [P]
    C. Peters: Monodromy and Picard-Fuchs equations for families of K3-surfaces and elliptic curves, Ann. Scient. Éc. Norm. Sup. 4.e ser. 19, 1986, 583–607.MathSciNetMATHGoogle Scholar
  6. [Po]
    A.J. van der Poorten: A proof that Euler missed.. Apéy's proof of the irrationality of ζ(3), Math. Intell., 1, 1979, 195–203.CrossRefMATHGoogle Scholar
  7. [R]
    H. Rademacher, Topics in analytic number theory, Springer Verlag 1973.Google Scholar
  8. [S-B]
    J. Stienstra, F. Beukers: On the Picard-Fuchs equation and the formal Brauer group of certain elliptic K3-surfaces, Math. Ann., 271, 1985, 269–304.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • C. Peters
    • 1
    • 2
  • J. Steinstra
    • 1
    • 2
  1. 1.Math. Inst. Rijksuniversiteit LeidenLeidenThe Netherlands
  2. 2.Math. Inst. Rijksuniversiteit UtrechtUtrechtThe Netherlands

Personalised recommendations