论文标题
部分可观测时空混沌系统的无模型预测
Complete Description of Measures Corresponding to Abelian Varieties over Finite Fields
论文作者
论文摘要
我们研究了与有限领域的阿贝尔品种家族相对应的概率度量。这些措施在TSFASMAN-VLADUTS理论中起着重要作用，该理论完全定义了家族的极限Zeta功能。 J.-P.Serre使用R.M.Robinson在共轭代数整数上的结果描述了可能的度量集，而不是对应于有限场上的Abelian品种家族。是否实际发生所有此类措施的问题是打开的。此外，Serre认为并非所有此类措施都与Abelian品种相对应（例如，在细分市场上的Lebesgue度量）。在这里，我们解决了Serre的问题，证明了Serre条件足够，因此完全描述了与Abelian品种相对应的一组措施。
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.
