$\mathbf{Li}^{\boldsymbol{(p)}}$-service? An algorithm for computing $\boldsymbol{p}$-adic polylogarithms

DOI10.1090/S0025-5718-07-02027-3zbMath1183.11037OpenAlexW1490957844MaRDI QIDQ5444320

Amnon Besser, Rob de Jeu

Publication date: 25 February 2008

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-02027-3

zbMATH Keywords

Coleman integrationcomputational number theory\(p\)-adic polylogarithm

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Polylogarithms and relations with (K)-theory (11G55)

Related Items (8)

Explicit Chabauty-Kim theory for the thrice punctured line in depth 2 ⋮ Mixed Tate motives and the unit equation. II ⋮ Refined Selmer equations for the thrice-punctured line in depth two ⋮ Explicit Coleman integration for curves ⋮ The polylog quotient and the Goncharov quotient in computational Chabauty–Kim theory II ⋮ Explicit Coleman Integration for Hyperelliptic Curves ⋮ A non-abelian conjecture of Tate-Shafarevich type for hyperbolic curves ⋮ The polylog quotient and the Goncharov quotient in computational Chabauty–Kim Theory I

Cites Work

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• On the \(p\)-adic Beilinson conjecture for number fields
• Dilogarithms, regulators and \(p\)-adic \(L\)-functions
• Montgomery multiplication in \(\text{GF}(2^ k)\)
• Rigid analytic geometry and its applications
• Modular Multiplication Without Trial Division
• The syntomic regulator for the K-theory of fields
• Syntomic regulators and \(p\)-adic integration. I: Rigid syntomic regulators

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