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Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields

  • Jeffrey Achter (a1) and Cassandra Williams (a2)

Consider a quartic q-Weil polynomial Ζ’. Motivated by equidistribution considerations, we define, for each prime β„“, a local factor that measures the relative frequency with which Ζ’ mod β„“ occurs as the characteristic polynomial of a symplectic similitude over 𝔽ℓ. For a certain class of polynomials, we show that the resulting infinite product calculates the number of principally polarized abelian surfaces over 𝔽 q with Weil polynomial Ζ’.

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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