The Points of a Certain Fivefold over Finite Fields and the Twelfth Power of the Eta Function

  • Authors:

  • Scott Ahlgren

  • Affiliations:

  • Department of Mathematics, Colgate University, Hamilton, New York, 13346, f1sahlgren@mail.colgate.eduf1

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2002

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Abstract

If p is an odd prime, then denote by F"p the field with p elements. We prove that a certain fivefold is modular in the sense that for every odd p, the number of its points over F"p is predicted explicitly by the pth coefficient of the Fourier expansion of the weight 6 modular form @h^1^2(2z).