Distribution of Farey fractions in residue classes and Lang--Trotter conjectures on average
نویسندگان
چکیده
منابع مشابه
Distribution of Farey Fractions in Residue Classes and Lang–Trotter Conjectures on Average
We prove that the set of Farey fractions of order T , that is, the set {α/β ∈ Q : gcd(α, β) = 1, 1 ≤ α, β ≤ T}, is uniformly distributed in residue classes modulo a prime p provided T ≥ p1/2+ε for any fixed ε > 0. We apply this to obtain upper bounds for the Lang–Trotter conjectures on Frobenius traces and Frobenius fields “on average” over a one-parametric family of elliptic curves.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09324-6