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

Part of the Lecture Notes in Mathematics book series (LNM,volume 1399)

Keywords

  • Fermi Surface
  • Fundamental Domain
  • Cusp Form
  • Hodge Structure
  • Monodromy Group

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References

  1. F. Beukers: Another congruence for the Apéry numbers, Journ. of Number Theory, 25, 1987, 201–210.

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  2. F. Beukers: Irrationality proofs using modular forms. Journées Arithm. Besançon (1985), Astérisque, 147, 1987, 271–283, 345.

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  3. F. Beukers, C. Peters: A family of K3-surfaces and ζ(3), Journ. f. reine u. angew. Math., 351, 1984, 42–54.

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  4. D. Gieseker, H. Knörrer, E. Trubowitz: Fermi curves and density of states, forthcoming.

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  5. 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.

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  6. 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.

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  7. H. Rademacher, Topics in analytic number theory, Springer Verlag 1973.

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  8. 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.

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© 1989 Springer-Verlag

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Peters, C., Steinstra, J. (1989). A pencil of K3- surfaces related to Apéry's recurrence for ζ(3) and Fermi surfaces for potential zero. In: Barth, WP., Lange, H. (eds) Arithmetic of Complex Manifolds. Lecture Notes in Mathematics, vol 1399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095972

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  • DOI: https://doi.org/10.1007/BFb0095972

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  • Print ISBN: 978-3-540-51729-0

  • Online ISBN: 978-3-540-46791-5

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