TY - JOUR

T1 - Distribution of farey fractions in residue classes and lang-trotter conjectures on average

AU - Cojocaru, Alina Carmen

AU - Shparlinski, Igor E.

N1 - Copyright 2008 American Mathematical Society. First published in Proceedings of the American Mathematical Society, Vol 136, Iss 6, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9939-08-09324-6

PY - 2008/6

Y1 - 2008/6

N2 - 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+∈ for any fixed ∈ > 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.

AB - 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+∈ for any fixed ∈ > 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.

UR - http://www.scopus.com/inward/record.url?scp=68949191312&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09324-6

DO - 10.1090/S0002-9939-08-09324-6

M3 - Article

AN - SCOPUS:68949191312

VL - 136

SP - 1977

EP - 1986

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -