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Numerical
evidence on the uniform distribution of power residues for
elliptic curves
Jeffrey Hatley and Amanda Hittson
Vol. 2 (2009), No. 3, 305–321
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Abstract |
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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 and a prime , denote by the number of points on over the finite field . It has been conjectured that given an elliptic curve without complex multiplication and any modulus , the primes for which is a square modulo are uniformly distributed among the residue classes modulo . This paper offers numerical evidence in support of this conjecture. |
Keywords
elliptic curve, power residue, uniform distribution,
computational algebraic geometry
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Mathematical Subject Classification 2000
Primary: 11Y99
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Milestones
Received: 21 September 2008
Revised: 1 April 2009
Accepted: 11 April 2009
Published: 3 October 2009
Communicated by Nigel Boston
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Authors |
| Jeffrey Hatley | |
| Department of Mathematics University of Massachusetts Amherst, MA 01003-9305 United States |
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| Amanda Hittson | |
| Department of Mathematics University of Wisconsin 480 Lincoln Drive Madison, WI 53706-1388 United States |
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