Computing Class Polynomials for Abelian Surfaces

We describe a quasilinear algorithm for computing Igusa class polynomials of Jacobians of genus-2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Du...

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Veröffentlicht in:	Experimental mathematics 2014-04, Vol.23 (2), p.129-145
Hauptverfasser:	Enge, Andreas, Thomé, Emmanuel
Format:	Artikel
Sprache:	eng
Schlagworte:	abelian varieties of dimension >1 algebraic number theory computations applications to coding theory and cryptography complex multiplication Computer Science Cryptography and Security Mathematics Number Theory theta functions
Online-Zugang:	Volltext
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