On the Distribution of the Number of Points on Elliptic Curves in a Tower of Extentions of Finite Fields
نویسندگان
چکیده
Let C be a smooth absolutely irreducible curve of genus g ≥ 1 defined over Fq, the finite field of q elements, and let #C(Fqn) be the number of Fqn-rational points on C. Under a certain condition, which, for example, satisfied by all ordinary elliptic curves, we obtain an asymptotic formula for the number of ratios (#C(Fqn)−q−1)/2gq, n = 1, . . . , N , inside of a given interval I ⊆ [−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.
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