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- W747246285 abstract "Let $cC$ be a smooth absolutely irreducible curve of genus $g ge 1$ defined over $F_q$, the finite field of $q$ elements. Let $# cC(F_{q^n})$ be the number of $F_{q^n}$-rational points on $cC$. Under a certain multiplicative independence condition on the roots of the zeta-function of $cC$, we derive an asymptotic formula for the number of $n =1, ..., N$ such that $(# cC(F_{q^n}) - q^n -1)/2gq^{n/2}$ belongs to a given interval $cI subseteq [-1,1]$. This can be considered as an analogue of the Sato-Tate distribution which covers the case when the curve $E$ is defined over $Q$ and considered modulo consecutive primes $p$, although in our scenario the distribution function is different. The above multiplicative independence condition has, recently, been considered by E. Kowalski in statistical settings. It is trivially satisfied for ordinary elliptic curves and we also establish it for a natural family of curves of genus $g=2$." @default.
- W747246285 created "2016-06-24" @default.
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- W747246285 date "2009-07-21" @default.
- W747246285 modified "2023-09-26" @default.
- W747246285 title "On the Distribution of the Number of Points on Elliptic Curves in a Tower of Extensions of Finite Fields" @default.
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