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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)

Keywords

Fermi Surface Fundamental Domain Cusp Form Hodge Structure Monodromy Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Be]
    F. Beukers: Another congruence for the Apéry numbers, Journ. of Number Theory, 25, 1987, 201–210.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [Be2]
    F. Beukers: Irrationality proofs using modular forms. Journées Arithm. Besançon (1985), Astérisque, 147, 1987, 271–283, 345.MathSciNetzbMATHGoogle 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.MathSciNetzbMATHGoogle 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.MathSciNetzbMATHGoogle 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.CrossRefzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle 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

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