Class numbers of cyclotomic function fields

DOI10.1090/S0002-9947-99-02325-9zbMath0929.11049OpenAlexW1504177582MaRDI QIDQ4257589

Li Guo, Linghsueh Shu

Publication date: 31 August 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02325-9

zbMATH Keywords

class numberscongruence relationsCarlitz-Hayes cyclotomic function fieldlower bound for \(\ell\)-partstower of Carlitz cyclotomic extensions

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23)

Related Items (8)

Class number growth of a family of \(\mathbb{Z}_p\)-extensions over global function fields ⋮ Infinite class towers for function fields ⋮ On the subfields of cyclotomic function fields ⋮ Infinite families of cyclotomic function fields with any prescribed class group rank ⋮ Iwasawa main conjecture for the Carlitz cyclotomic extension and applications ⋮ On the Deuring-Shafarevich formula ⋮ On the \(p\)-divisibility of class numbers of cyclotomic function fields ⋮ Demjanenko matrix and recursion formula for relative class number over function fields.

Cites Work

• Unnamed Item
• On geometric \({\mathbb{Z}}_ p\)-extensions of function fields
• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• Units and class groups in cyclotomic function fields
• A class number formula for cyclotomic fields
• On \(p\)-adic \(L\)-functions
• On certain functions connected with polynomials in a Galois field

This page was built for publication: Class numbers of cyclotomic function fields