Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height
By William D. Banks, Igor E. Shparlinski. 2006
54 citations recorded by the source corpus.
AbstractWe obtain asymptotic formulae for the number of primes p ≤ 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 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/11bc8d8ed03d6d0e0b6ffedcbe6d464f43ffa9e5
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Average twin prime conjecture for elliptic curves (2007, methodology): “2+" [Bai] by using an average result on character sums of [ BaSh ], which is a consequence of a more general result of [Gar].”