Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height
| dc.creator | Banks, William D. | |
| dc.creator | Shparlinski, Igor E. | |
| dc.date | 2006-09-05 | |
| dc.date | 2007-11-26 | |
| dc.date.accessioned | 2026-07-07T08:44:43Z | |
| dc.date.available | 2026-07-07T08:44:43Z | |
| dc.description | We obtain asymptotic formulae for the number of primes $p\le x$ for which the reduction modulo $p$ of the elliptic curve $$ \E_{a,b} : Y^2 = X^3 + aX + b $$ satisfies certain ``natural'' properties, on average over integers $a$ and $b$ with $|a|\le A$ and $|b| \le B$, where $A$ and $B$ are small relative to $x$. Specifically, we investigate behavior with respect to the Sato--Tate conjecture, cyclicity, and divisibility of the number of points by a fixed integer $m$. | |
| dc.identifier | https://arxiv.org/abs/math/0609144 | |
| dc.identifier | http://arxiv.org/abs/math/0609144 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142755 | |
| dc.subject | Number Theory | |
| dc.subject | 11G05, 11L40, 14H52 | |
| dc.title | Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height | |
| dc.type | text |