On the class numbers of the maximal real subfields of cyclotomic function fields

DOI10.1006/ffta.1998.0208zbMath0920.11075OpenAlexW2156789757MaRDI QIDQ1266995

Humio Ichimura

Publication date: 31 August 1999

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.1998.0208

zbMATH Keywords

function fieldsclass numberscyclotomic fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (7)

Biographical Sketch of Professor Humio Ichimura ⋮ On real quadratic function fields ⋮ On normal integral bases of unramified abelian \(p\)-extensions over a global function field of characteristic \(p\) ⋮ Infinite families of cyclotomic function fields with any prescribed class group rank ⋮ On the class numbers of the maximal real subfields of cyclotomic function fields. II ⋮ Corrigendum: On the class groups of pure function fields ⋮ Infinite families of irregular primes in cyclotomic function fields

Cites Work

• On regularity of small primes in function fields
• Class-groups of function fields
• A note on irregular prime polynomials in cyclotomic function field theory
• Class numbers of cyclotomic fields
• The Hilbert class field in function fields
• Kummer and Herbrand criterion in the theory of function fields
• Units and class groups in cyclotomic function fields
• Analytische Zahlentheorie in Körpern der Charakteristik \(p\)
• Class number and ramification in fields of algebraic functions
• \(S\)-units and \(S\)-class group in algebraic function fields
• Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
• Explicit Class Field Theory for Rational Function Fields
• Class Number Computations of Real Abelian Number Fields
• On the class-number of the maximal real subfield of a cyclotomic field.
• Almost-primes represented by quadratic polynomials
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