On 𝑃-orderings, rings of integer-valued polynomials, and ultrametric analysis

DOI10.1090/S0894-0347-09-00638-9zbMath1219.11047MaRDI QIDQ3058270

Manjul Bhargava

Publication date: 19 November 2010

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

integer-valued polynomialsfactorial function\(p\)-adic analysisultrametric analysis\(P\)-ordering

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Polynomials over commutative rings (13B25)

Related Items (19)

On algorithms to find \(p\)-ordering ⋮ Algebraic-integer valued polynomials ⋮ Bhargava’s Early Work: The Genesis of <em>P</em>-Orderings ⋮ What You Should Know About Integer-Valued Polynomials ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ The factorial function and generalizations, extended ⋮ The Bhargava greedoid ⋮ Integer valued polynomials on lower triangular integer matrices ⋮ Regular subsets of valued fields and Bhargava's \(v\)-orderings ⋮ Integer-valued polynomials over matrices and divided differences ⋮ Bhargava rings that are Prüfer v-multiplication domains ⋮ 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> ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ Finite generation properties for various rings of integer-valued polynomials ⋮ A greedoid and a matroid inspired by Bhargava's \(p\)-orderings ⋮ Super-additive sequences and algebras of polynomials ⋮ Functions with integer-valued divided differences ⋮ About Polynomials Whose Divided Differences are Integer-Valued on Prime Numbers ⋮ The ring of polynomials integral-valued over a finite set of integral elements

Cites Work

• Finite generation properties for various rings of integer-valued polynomials
• Polynomials over GF(q,x) with integral-valued differences
• Locally analytic functions over completions of \(\mathbb F_r[U\)]
• On the ultrametric Stone-Weierstrass theorem and Mahler's expansion
• Rigid analytic geometry and its applications
• Polynomial mappings
• The Factorial Function and Generalizations
• Integer-Valued Polynomials
• Anneaux de Bhargava
• An Interpolation Series for Continuous Functions of a p-adic Variable.
• Fonctions $k$-lipschitziennes sur un anneau local et polynômes à valeurs entières
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• Continuous functions on compact subsets of local fields
• Interpolation $p$-adique
• Interpolation series for continuous functions on π-adic completions of GF(q, x)
• Polynomes a Valeurs Entieres
• The Weierstrass Theorem in Fields with Valuations
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