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THE CUBIC CONGRUENCE x3 + Ax2 + Bx + C ≡ 0 (mod p) AND BINARY QUADRATIC FORMS II

Published online by Cambridge University Press:  30 October 2001

BLAIR K. SPEARMAN  and
KENNETH S. WILLIAMS
BLAIR K. SPEARMAN
Affiliation:
Department of Mathematics and Statistics, Okanagan University College, Kelowna, British Columbia V1V 1V7, Canada; bkspearm@okuc02.okanagan.bc.ca
KENNETH S. WILLIAMS
Affiliation:
Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada; williams@math.carleton.ca
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Abstract

It is shown that the splitting modulo a prime p of a given monic, integral, irreducible cubic with non-square discriminant is equivalent to p being represented by forms in a certain subgroup of index 3 in the form class group of discriminant equal to the discriminant of the field defined by the cubic.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 273 - 274
Copyright
The London Mathematical Society 2001

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