Abelian subgroups of any order in class groups of global function fields

DOI10.1016/j.jnt.2003.12.003zbMath1100.11039OpenAlexW2059757871MaRDI QIDQ1434334

Allison M. Pacelli

Publication date: 4 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2003.12.003

zbMATH Keywords

Function fieldClass numberClass group

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Class numbers, class groups, discriminants (11R29)

Related Items

The prime at infinity and the rank of the class group in global function fields ⋮ Decomposition of places in dihedral and cyclic quintic trinomial extensions of global fields ⋮ The global Cohen-Lenstra heuristic ⋮ Construction of hyperelliptic function fields of high three-rank ⋮ Higher rank subgroups in the class groups of imaginary function fields ⋮ Class groups of global function fields with certain splitting behaviors of the infinite prime ⋮ A family of quintic cyclic fields with even class number parameterized by rational points on an elliptic curve ⋮ The distribution of class groups of function fields

Cites Work

• On the class groups of pure function fields
• On unramified Galois extensions of quadratic number fields
• On ideal groups of algebraic number fields.
• Class Number Divisibility in Real Quadratic Function Fields
• A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn
• Exponents of Class Groups of Quadratic Function Fields over Finite Fields
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