The Scholz theorem in function fields

DOI10.1016/j.jnt.2006.05.014zbMath1155.11052OpenAlexW1982614568MaRDI QIDQ1005556

Yoon-Jin Lee

Publication date: 9 March 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.05.014

zbMATH Keywords

rankclass groupsregulatorimaginary quadratic function fieldsreal quadratic function fieldscyclic function fieldsScholz theorem

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Class numbers, class groups, discriminants (11R29)

Related Items (3)

Construction of all cubic function fields of a given square-free discriminant ⋮ Infinite families of class groups of quadratic fields with 3-rank at least one: quantitative bounds ⋮ Computing quadratic function fields with high 3-rank via cubic field tabulation

Cites Work

• The Hilbert class field in function fields
• Cohen-Lenstra heuristics and the Spiegelungssatz: function fields
• \(S\)-units and \(S\)-class group in algebraic function fields
• A quadratic field of prime discriminant requiring three generators for its class group, and related theory
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