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p-adic class invariants

Part of: Arithmetic algebraic geometry Computational number theory

Published online by Cambridge University Press:  01 April 2011

Reinier Bröker
Reinier Bröker*
Affiliation:
Brown University, Box 1917, 151 Thayer Street Providence, RI, USA (email: reinier@math.brown.edu)

Abstract

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We develop a new p-adic algorithm to compute the minimal polynomial of a class invariant. Our approach works for virtually any modular function yielding class invariants. The main algorithmic tool is modular polynomials, a concept which we generalize to functions of higher level.

MSC classification

Secondary: 11G15: Complex multiplication and moduli of abelian varieties 11Y40: Algebraic number theory computations
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 108 - 126
Copyright
Copyright © London Mathematical Society 2011

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