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2009 Numerical evidence on the uniform distribution of power residues for elliptic curves
Jeffrey Hatley, Amanda Hittson
Involve 2(3): 305-321 (2009). DOI: 10.2140/involve.2009.2.305

Abstract

Elliptic curves are fascinating mathematical objects which occupy the intersection of number theory, algebra, and geometry. An elliptic curve is an algebraic variety upon which an abelian group structure can be imposed. By considering the ring of endomorphisms of an elliptic curve, a property called complex multiplication may be defined, which some elliptic curves possess while others do not. Given an elliptic curve E and a prime p, denote by Np the number of points on E over the finite field Fp. It has been conjectured that given an elliptic curve E without complex multiplication and any modulus M, the primes for which Np is a square modulo p are uniformly distributed among the residue classes modulo M. This paper offers numerical evidence in support of this conjecture.

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Jeffrey Hatley. Amanda Hittson. "Numerical evidence on the uniform distribution of power residues for elliptic curves." Involve 2 (3) 305 - 321, 2009. https://doi.org/10.2140/involve.2009.2.305

Information

Received: 21 September 2008; Revised: 1 April 2009; Accepted: 11 April 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1195.11077
MathSciNet: MR2551128
Digital Object Identifier: 10.2140/involve.2009.2.305

Subjects:
Primary: 11Y99

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.2 • No. 3 • 2009
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