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Bhargava, Manjul

On \(P\)-orderings, rings of integer-valued polynomials, and ultrametric analysis. (English) Zbl 1219.11047

J. Am. Math. Soc. 22, No. 4, 963-993 (2009).
The author introduces two new notions of “\(P\)-ordering” and use them to define a three-parameter generalization of the factorial function. He constructs explicit Pólya-style regular bases for two natural families of rings of integer-valued polynomials defined on an arbitrary subset of a Dedekind domain and explicit interpolation series for the Banach space of functions on an arbitrary compact subset of a local field satisfying conditions of continuous differentiability or local analyticity, obtaining the non-Archimedean analogues of the classical polynomial approximation theorems in real and complex analysis.
Reviewer: Florin Nicolae (Berlin)

Cited in 5 Reviews
Cited in 22 Documents

MSC:

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

Keywords:

\(P\)-ordering; factorial function; integer-valued polynomials; \(p\)-adic analysis; ultrametric analysis
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Full Text: DOI

References:

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