On some questions related to the Gauss conjecture for function fields

DOI10.1016/j.jnt.2007.10.014zbMath1221.11190OpenAlexW2096263432WikidataQ122961297 ScholiaQ122961297MaRDI QIDQ958709

Régis Blache, Yves Aubry

Publication date: 8 December 2008

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2007.10.014

zbMATH Keywords

Jacobianfinite fieldsGauss conjecturehyperelliptic curveszeta functionsfunctions fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29) Zeta and (L)-functions in characteristic (p) (11M38) Algebraic functions and function fields in algebraic geometry (14H05)

Cites Work

• Unnamed Item
• On \(L\)-functions of cyclotomic function fields
• The generic irreducibility of the numerator of the zeta function in a family of curves with large monodromy
• Endomorphisms of Abelian varieties over finite fields
• The large sieve, monodromy and zeta functions of curves
• Jacobi Sums, Irreducible Zeta-Polynomials, and Cryptography
• Gauss problem for function fields
• On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field

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