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Mathematics of Computation

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Bounds for the smallest norm in an ideal class

Author: Ana-Cecilia de la Maza
Journal: Math. Comp. 71 (2002), 1745-1758
MSC (2000): Primary 11R29; Secondary 11Y60
Published electronically: October 26, 2001
MathSciNet review: 1933053
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Abstract: We develop a method for obtaining upper bounds for the smallest norm among all norms of integral ideals in an ideal class. Applying this to number fields of small degree, we are able to substantially improve on the best previously known bounds.

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Additional Information

Ana-Cecilia de la Maza
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

Keywords: Ideal classes of number fields, norm bounds, Minkowski's constant
Received by editor(s): September 15, 1999
Received by editor(s) in revised form: December 26, 2000
Published electronically: October 26, 2001
Additional Notes: This work was supported by Fondecyt grants N$^{\mathrm o}$ 2950023, 1960867 and 1981170, and by Programa formas extremas y representación de formas cuadráticas, Universidad de Talca, Chile
Article copyright: © Copyright 2001 American Mathematical Society