Units and class groups in cyclotomic function fields

DOI10.1016/0022-314X(82)90045-2zbMath0483.12003MaRDI QIDQ1163056

Steven Galovich, Michael I. Rosen

Publication date: 1982

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

zbMATH Keywords

class numbercyclotomic function fieldcircular unitsmaximal real subfieldKummer theorem

Mathematics Subject Classification ID

Units and factorization (11R27) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18)

Related Items (28)

Cyclotomic units and Stickelberger ideals of global function fields ⋮ On the index of cyclotomic units in characteristic \(p\) and its applications ⋮ The refined \(\mathfrak p\)-adic abelian Stark conjecture in function fields ⋮ Growth order and congruences of coefficients of the Drinfeld discriminant function ⋮ David R. Hayes: some remarks on his life and work ⋮ Idéaux ambiges dans les corps de fonctions. (Ambiguous ideals in function fields) ⋮ The \(q\)-unit circle: the unit circle in prime characteristics and its properties ⋮ A rapid introduction to Drinfeld modules, \(t\)-modules, and \(t\)-motives ⋮ Division algebras and maximal orders for given invariants ⋮ Distributions on rational function fields ⋮ Analytic class number formulas in function fields ⋮ Stickelberger ideals and relative class numbers in function fields ⋮ Bases for cyclotomic units over function fields ⋮ Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields ⋮ On the subfields of cyclotomic function fields ⋮ Circular Units of Function Fields ⋮ Determinant formulas for class numbers in function fields ⋮ Unnamed Item ⋮ Kummer theory of division points over Drinfeld modules of rank one ⋮ Cyclotomic function fields with ideal class number one ⋮ Punctured distributions in the rational function fields ⋮ Explicit Galois representations of automorphisms on holomorphic differentials in characteristic \(p\) ⋮ On the class numbers of the maximal real subfields of cyclotomic function fields ⋮ On the class group problem for function fields ⋮ Class numbers of cyclotomic function fields ⋮ The arithmetic of function fields. II: The 'cyclotomic' theory ⋮ Class number one problem for imaginary function fields: the cyclic prime power case ⋮ Kummer's theory for function fields

Cites Work

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• The \(\Gamma\)-ideal and special zeta-values
• The class number of cyclotomic function fields
• On the Stickelberger ideal and the circular units of a cyclotomic field
• \(S\)-units and \(S\)-class group in algebraic function fields
• Explicit Class Field Theory for Rational Function Fields
• ELLIPTIC MODULES
• The universal ordinary distribution
• The Z/2 Z cohomology of the universal ordinary distribution

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