TY - JOUR

T1 - Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height

AU - Banks, William D.

AU - Shparlinski, Igor E.

PY - 2009/1

Y1 - 2009/1

N2 - We obtain asymptotic formulae for the number of primes p ≤ x for which the reduction modulo p of the elliptic curve satisfies certain "natural" properties, on average over integers a and b such that |a| ≤ A and |b| ≤ B, where A and B are small relative to x. More precisely, we investigate behavior with respect to the Sato-Tate conjecture, cyclicity, and divisibility of the number of points by a fixed integer m.

AB - We obtain asymptotic formulae for the number of primes p ≤ x for which the reduction modulo p of the elliptic curve satisfies certain "natural" properties, on average over integers a and b such that |a| ≤ A and |b| ≤ B, where A and B are small relative to x. More precisely, we investigate behavior with respect to the Sato-Tate conjecture, cyclicity, and divisibility of the number of points by a fixed integer m.

UR - http://www.scopus.com/inward/record.url?scp=70350028319&partnerID=8YFLogxK

U2 - 10.1007/s11856-009-0091-0

DO - 10.1007/s11856-009-0091-0

M3 - Article

AN - SCOPUS:70350028319

VL - 173

SP - 253

EP - 277

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -