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
SN - 0021-2172
VL - 173
SP - 253
EP - 277
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -