Gauss problem for function fields

DOI10.1006/jnth.2000.2523zbMath1014.11072OpenAlexW2074666070MaRDI QIDQ5928000

S. G. Vleduts, Gilles Lachaud

Publication date: 19 March 2001

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

Full work available at URL: https://semanticscholar.org/paper/a2cb4089761fdf67cc49417fafd17f487e788520

zbMATH Keywords

class field towerclass numbercongruence function fieldsDrinfeld modular curvesGauss conjectureideal class numbermodular curvesring of \(S\)-integers

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Arithmetic aspects of modular and Shimura varieties (11G18) [https://portal.mardi4nfdi.de/w/index.php?title=+Special%3ASearch&search=%22Curves+of+arbitrary+genus+or+genus+%28%0D%0Ae+1%29+over+global+fields%22&go=Go Curves of arbitrary genus or genus ( e 1) over global fields (11G30)] Class field theory (11R37) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60)

Related Items (2)

Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud ⋮ On some questions related to the Gauss conjecture for function fields

Cites Work

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• Algebraic function fields and codes
• The Hilbert class field in function fields
• Algebraic curves over \({\mathbb{F}}_ 2\) with many rational points
• Tours ramifiées infinies de corps de classes. (Infinite ramified class field towers)
• Infinitely many real quadratic fields of class number one
• Coverings of singular curves over finite fields
• Note on a problem of S. Chowla
• On unique factorization in certain rings of algebraic functions
• \(S\)-units and \(S\)-class group in algebraic function fields
• Estimates of regulators and class numbers in function fields.

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