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September 2014 Explicit congruences for class equations
Patrick Morton
Funct. Approx. Comment. Math. 51(1): 77-110 (September 2014). DOI: 10.7169/facm/2014.51.1.4

Abstract

Explicit congruences (mod $p$) are proved for the class equations corresponding to discriminants $D=-8p, -3p, -12p$ in the theory of complex multiplication, where $p$ is an odd prime. They are explicit in that they can be computed directly from a formula for the supersingular polynomial without first having to know the coefficients of the class equation in characteristic zero. These congruences have previously appeared in print without proof, and have been used to study factorizations of certain Legendre polynomials (mod $p$).

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Patrick Morton. "Explicit congruences for class equations." Funct. Approx. Comment. Math. 51 (1) 77 - 110, September 2014. https://doi.org/10.7169/facm/2014.51.1.4

Information

Published: September 2014
First available in Project Euclid: 24 September 2014

zbMATH: 1364.11112
MathSciNet: MR3263070
Digital Object Identifier: 10.7169/facm/2014.51.1.4

Subjects:
Primary: 11G15
Secondary: 11H52, 11R11

Rights: Copyright © 2014 Adam Mickiewicz University

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Vol.51 • No. 1 • September 2014
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