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Uniform distribution of the Steinitz invariants of quadratic and cubic extensions

Published online by Cambridge University Press:  13 January 2006

Anthony C. Kable  and
David J. Wright
Anthony C. Kable
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater OK 74078, [email protected]
David J. Wright
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater OK 74078, [email protected]
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Abstract

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It is shown that the Steinitz invariants of the cubic extensions of a number field are uniformly distributed in the class group when the cubic extensions are ordered by the ideal norm of their relative discriminants. This remains true even if the extensions are restricted by specifying their splitting type at a finite number of places. The same statement is also proved for quadratic extensions.

Keywords

Steinitz invariantcubic extensionequidistributionShintani zeta function11R45 (primary)11R1111R1611S9011M41 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 84 - 100
Copyright
Foundation Compositio Mathematica 2006