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- W4313447740 abstract "We study probability measures corresponding to families of abelian varieties over a finite field. These measures play an important role in the Tsfasman- Vladuts theory of asymptotic zeta-functions defining completely the limit zeta-function of the family. J.-P.Serre, using results of R.M.Robinson on conjugate algebraic integers, described the possible set of measures than can correspond to families of abelian varieties over a finite field. The problem whether all such measures actually occur was left open. Moreover, Serre supposed that not all such measures correspond to abelian varieties (for example, the Lebesgue measure on a segment). Here we settle Serre's problem proving that Serre conditions are sufficient, and thus describe completely the set of measures corresponding to abelian varieties." @default.
- W4313447740 created "2023-01-06" @default.
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- W4313447740 date "2022-12-30" @default.
- W4313447740 modified "2023-09-24" @default.
- W4313447740 title "Complete Description of Measures Corresponding to Abelian Varieties over Finite Fields" @default.
- W4313447740 doi "https://doi.org/10.48550/arxiv.2212.14854" @default.
- W4313447740 hasPublicationYear "2022" @default.
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