Simultaneous orderings in function fields

DOI10.1016/j.jnt.2004.11.015zbMath1075.11075OpenAlexW1989531060MaRDI QIDQ557564

David Adam

Publication date: 30 June 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.11.015

zbMATH Keywords

integer-valued polynomialsquadratic function fieldsimultaneous ordering

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Valuations and their generalizations for commutative rings (13A18) Polynomials (irreducibility, etc.) (11R09) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (10)

On Bhargava's factorials of the set of twin primes in ℤ and in 𝔽_q[T] ⋮ Integer-Valued Polynomials: Looking for Regular Bases (A Survey) ⋮ Pólya and Newtonian function fields ⋮ Fixed Divisor of a Multivariate Polynomial and Generalized Factorials in Several Variables ⋮ Newtonian and Schinzel quadratic fields ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ Newton and Schinzel sequences in quadratic fields ⋮ Polynomial functions in the residue class rings of Dedekind domains ⋮ Newtonian and Schinzel sequences in a domain ⋮ A survey on fixed divisors

Cites Work

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• Generalized factorials and fixed divisors over subsets of a Dedekind domain
• \(P\)-orderings: A metric viewpoint and the non-existence of simultaneous orderings.
• Asymptotic behavior of characteristic sequences of integer-valued polynomials
• The Factorial Function and Generalizations
• Integer-Valued Polynomials
• Une Caractérisation des Polynômes Prenant des Valeurs Entières Sur Tous les Nombres Premiers
• P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
• Répartition modulo 1 dans un corps de séries formelles sur un corps fini

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