Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average

Details Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average

2007-05-25

arxiv.org/abs/0705.3861v1

Mathematics

Number Theory

Scientific paper

We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any fixed $\eps>0$. 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.

Affiliated with

Also associated with

No associations

Rating

Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-582059