Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average
| dc.creator | Cojocaru, A. C. | |
| dc.creator | Shparlinski, I. E. | |
| dc.date | 2007-05-25 | |
| dc.date.accessioned | 2026-07-07T08:03:17Z | |
| dc.date.available | 2026-07-07T08:03:17Z | |
| dc.description | We prove that the set of Farey fractions of order $T$, that is, the set $\{α/β\in \Q : \gcd(α, β) = 1, 1 \le α, β\le T\}$, 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. | |
| dc.identifier | https://arxiv.org/abs/0705.3861 | |
| dc.identifier | http://arxiv.org/abs/0705.3861 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129526 | |
| dc.subject | Number Theory | |
| dc.subject | 11B57, 11G07, 14H52 | |
| dc.title | Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average | |
| dc.type | text |