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Journal of the London Mathematical Society 1992 s2-46(3):397-410; doi:10.1112/jlms/s2-46.3.397
© 1992 by London Mathematical Society
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© Oxford University Press

The Cubic Congruence x3 + Ax2 + Bx + C {equiv} 0(mod p) and Binary Quadratic Forms

Blair K. Spearman and Kenneth S. Williams

Department of Mathematics, Okanagan College Kelowna, British Columbia, Canada VIY 4X8
Department of Mathematics and Statistics, Carleton University Ottawa, Ontario, Canada K1S 5B6

In this paper it is shown that the splitting modulo a prime p of a given monic irreducible cubic polynomial with integral coefficients 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 cubic.


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