Leading coefficient of the Goss Zeta value and p-ranks of Jacobians of Carlitz cyclotomic covers

DOI10.5802/jtnb.1008zbMath1430.11124OpenAlexW2793736878MaRDI QIDQ5374149

Dinesh S. Thakur, Gebhard Böckle

Publication date: 9 April 2018

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5802/jtnb.1008

zbMATH Keywords

Bernoulli numberpower sumHerbrand-Ribet theoremHasse-Witt invariantordinarinessArtin-Schreier polynomialCarlitz cyclotomic fieldGoss \(\zeta\)-function

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Zeta and (L)-functions in characteristic (p) (11M38) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (2)

Power sums of polynomials over finite fields and applications: a survey ⋮ Infinite families of irregular primes in cyclotomic function fields

Uses Software

• Magma
• Maple
• Maxima
• SageMath

Cites Work

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• Abelian varieties over finite fields
• On Multinomial Coefficients
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