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

Alina Carmen Cojocaru, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
6 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)1977-1986
Number of pages10
JournalProceedings of the American Mathematical Society
Volume136
Issue number6
DOIs
Publication statusPublished - Jun 2008

Bibliographical note

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

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