Power sums of polynomials over finite fields and applications: a survey

DOI10.1016/j.ffa.2014.08.004zbMath1378.11101OpenAlexW2083699712MaRDI QIDQ2512888

Dinesh S. Thakur

Publication date: 30 January 2015

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2014.08.004

zbMATH Keywords

zero distributionJacobianszetaBernoullimultizeta

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Jacobians, Prym varieties (14H40) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Arithmetic theory of polynomial rings over finite fields (11T55) Zeta and (L)-functions in characteristic (p) (11M38) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (7)

Goss polynomials, \(q\)-adic expansions, and Sheats compositions ⋮ A Carlitz-von Staudt type theorem for finite rings ⋮ A sum-shuffle formula for zeta values in Tate algebras ⋮ A conjectural characterization for \(\mathbb{F}_q(t)\)-linear relations between multizeta values ⋮ Iwasawa main conjecture for the Carlitz cyclotomic extension and applications ⋮ On twisted \(A\)-harmonic sums and Carlitz finite zeta values ⋮ Evaluation of some sums of polynomials in \(\mathbb{F}_q [t\)]

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