A proof of Pisot's dth root conjecture
成果类型：
Article
署名作者：
Zannier, U
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.2307/121122
发表日期：
2000
页码：
375-383
关键词：
摘要：
Let {b(n) : n is an element of N} be the sequence of coefficients in the Taylor expansion of a rational function R(X) is an element of Q(X) and suppose that b(n) is a perfect d(th) power for all large n. A conjecture of Pisot states that one can choose a d(th) root a(n) of b(n) such that Sigma a(n)X-n is also a rational function. Actually, this is the fundamental case of an analogous statement formulated for fields more general than Q. A number of papers have been devoted to various special cases. In this note we shall completely settle the general case.