Classification of polynomial mappings between commutative groups

JOURNAL OF NUMBER THEORY

卷:139

Article

Schauz, Uwe

关键词: Integer-valued polynomials;    Commutative groups;    Polynomial functions;    Polynomial mappings;    Interpolation;   

DOI  :  10.1016/j.jnt.2013.12.010

来源: Elsevier

【 摘 要 】

Some polynomials P with rational coefficients give rise to well defined maps between cyclic groups, Z(q) -> Z(r), x + qZ -> P(x) + rZ. More generally, there are polynomials in several variables with tuples of rational numbers as coefficients that induce maps between commutative groups. We characterize the polynomials with this property, and classify all maps between two given finite commutative groups that arise in this way. We also provide interpolation formulas and a Taylor-type theorem for the calculation of polynomials that describe given maps. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free