Questions About the Reductions Modulo Primes of an Elliptic Curve

By Alina Carmen Cojocaru. 2004

51 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/697fefc03713bb6bc4d9eb951074e85a5e111cd2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Igor E. Shparlinski
2. William D. Banks

In Geometry and Topology

1. William D. Banks
2. Igor E. Shparlinski
3. Richard A. Brualdi

In Information Systems

1. William D. Banks
2. Igor E. Shparlinski

Citations in the corpus

• Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height (2006, background): “…of primes p 6 x (with p ∤ 4a 3 +27b2) such that #Ea,b(Fp) = p+ 1 − t satisfies the asymptotic formula πa,b(t; x) ∼ ca,b,t · √ x log x (x→ ∞) with some constant ca,b,t that depends only on a, b, and t, provided that Ea,b does not have complex multiplication (see [44, Section III.4]) or t is nonzero.”