Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
