Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain

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Abstract

Given a subsetXof a Dedekind domainD, and a polynomialF∈D[x], thefixed divisor d(X, F) ofFoverXis defined to be the ideal inDgenerated by the elementsF(a),a∈X. In this paper we derive a simple expression ford(X, F) explicitly in terms of the coefficients ofF, using a generalized notion of "factorial" introduced by the author in a previous paper. WhenX=D=Z, this generalized factorial reduces to the ordinary factorial function; hence we obtain as special cases classic results of Pólya, Gunji, and McQuillan relatingd(Z, F) and the usual factorial function.

Original languageEnglish (US)
Pages (from-to)67-75
Number of pages9
JournalJournal of Number Theory
Volume72
Issue number1
DOIs
StatePublished - Sep 1 1998
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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