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
SN - 0002-9939
VL - 136
SP - 1977
EP - 1986
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 6
ER -