✦ LIBER ✦
Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain
✍ Scribed by Manjul Bhargava
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 202 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
Given a subset X of a Dedekind domain D, and a polynomial F # D[x], the fixed divisor d(X, F) of F over X is defined to be the ideal in D generated by the elements F(a), a # X. In this paper we derive a simple expression for d(X, F) explicitly in terms of the coefficients of F, using a generalized notion of ``factorial'' introduced by the author in a previous paper. When X=D=Z, this generalized factorial reduces to the ordinary factorial function; hence we obtain as special cases classic results of Po lya, Gunji, and McQuillan relating d(Z, F) and the usual factorial function.