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2011 On the Computation of Class Polynomials with “Thetanullwerte” and Its Applications to the Unit Group Computation
Franck Leprévost, Michael Pohst, Osmanbey Uzunkol
Experiment. Math. 20(3): 271-281 (2011).

Abstract

The classical class invariants of Weber are introduced as quotients of Thetanullwerte, enabling the computation of these invariants more efficiently than as quotients of values of the Dedekind η-function. We show also how to compute the unit group of suitable ring class fields by proving the fact that most of the invariants introduced by Weber are actually units in the corresponding ring class fields.

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Franck Leprévost. Michael Pohst. Osmanbey Uzunkol. "On the Computation of Class Polynomials with “Thetanullwerte” and Its Applications to the Unit Group Computation." Experiment. Math. 20 (3) 271 - 281, 2011.

Information

Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1269.11059
MathSciNet: MR2836252

Subjects:
Primary: 11G15 , 11Y35

Keywords: class fields , Complex Multiplication , Theta functions

Rights: Copyright © 2011 A K Peters, Ltd.

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Vol.20 • No. 3 • 2011
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