Regular subsets of valued fields and Bhargava's \(v\)-orderings

DOI10.1007/s00209-012-1069-xzbMath1270.13015OpenAlexW2049621202MaRDI QIDQ1955715

Jean-Luc Chabert, Sabine Evrard, Youssef Fares

Publication date: 18 June 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-012-1069-x

zbMATH Keywords

divided differencesinteger-valued polynomialsvalued fields\(v\)-orderingsregular subsetsvery well distributed sequences

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Valued fields (12J10)

Related Items (9)

What You Should Know About Integer-Valued Polynomials ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ Mahler's polynomial approximation for odd and even \(p\)-adic functions ⋮ Integer valued polynomials on lower triangular integer matrices ⋮ Test sets for polynomials: \(n\)-universal subsets and Newton sequences ⋮ Minimal Generating Sets for the D-Algebra Int(S, D) ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ Integer-valued polynomials, Prüfer domains and the stacked bases property ⋮ About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers

Cites Work

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• On the polynomial closure in a valued field
• Generalized factorials and fixed divisors over subsets of a Dedekind domain
• On the ultrametric Stone-Weierstrass theorem and Mahler's expansion
• On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis
• An Interpolation Series for Continuous Functions of a p-adic Variable.
• A correction to the paper An Interpolation Series for continuous functions of a p-adic variable.
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• Computing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>r</mml:mi></mml:math>-removed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>-orderings and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>P</mml:mi></mml:math>-orderings of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>h</mml:mi></mml:math>
• p -adic subsets whose factorials satisfy a generalized Legendre formula
• Interpolation $p$-adique

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