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Equidistribution of realizable Steinitz classes for cyclic Kummer extensions.

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Title: Equidistribution of realizable Steinitz classes for cyclic Kummer extensions.
Authors: Lynch, Brody1 (AUTHOR) bjlynch@umass.edu
Source: Journal of Number Theory. Apr2026, Vol. 281, p139-168. 30p.
Subjects: Algebraic number theory, Class groups (Mathematics), Galois theory, Scientific method
Abstract: Let ℓ be prime, and K be a number field containing the ℓ -th roots of unity. We use classical algebraic number theory and some analytic techniques to prove that the Steinitz classes of Z / ℓ Z extensions of K ordered by relative discriminant are equidistributed among realizable classes in the ideal class group of K. For ℓ = 2 , this was proved by Kable and Wright using the deep theory of prehomogeneous vector spaces. Foster proved that Steinitz classes are uniformly distributed between realizable classes for tamely ramified elementary- m extensions using the theory of Galois modules; our approach eliminates this tameness hypothesis. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 189762254
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  Data: Equidistribution of realizable Steinitz classes for cyclic Kummer extensions.
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  Data: <searchLink fieldCode="AR" term="%22Lynch%2C+Brody%22">Lynch, Brody</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bjlynch@umass.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Apr2026, Vol. 281, p139-168. 30p.
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  Label: Abstract
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  Data: Let ℓ be prime, and K be a number field containing the ℓ -th roots of unity. We use classical algebraic number theory and some analytic techniques to prove that the Steinitz classes of Z / ℓ Z extensions of K ordered by relative discriminant are equidistributed among realizable classes in the ideal class group of K. For ℓ = 2 , this was proved by Kable and Wright using the deep theory of prehomogeneous vector spaces. Foster proved that Steinitz classes are uniformly distributed between realizable classes for tamely ramified elementary- m extensions using the theory of Galois modules; our approach eliminates this tameness hypothesis. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.jnt.2025.09.022
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      – Code: eng
        Text: English
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        PageCount: 30
        StartPage: 139
    Subjects:
      – SubjectFull: Algebraic number theory
        Type: general
      – SubjectFull: Class groups (Mathematics)
        Type: general
      – SubjectFull: Galois theory
        Type: general
      – SubjectFull: Scientific method
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      – TitleFull: Equidistribution of realizable Steinitz classes for cyclic Kummer extensions.
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              Text: Apr2026
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              Y: 2026
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              Value: 281
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