Mahler-Lech定理[Mahler-Lech Theorem] - 达人(其实～我是卧底，来自外星)

2006/10/05 | Mahler-Lech定理[Mahler-Lech Theorem]
类别(∑〖数学〗) | 评论(0) | 阅读(92) | 发表于 21:49: Let be a field of field characteristic 0 (e.g., the rationals ) and let be a sequence of elements of which satisfies a difference equation of the form

where the coefficients are fixed elements of . Then, for any , we have either for only finitely many values of , or for the values of in some arithmetic progression.

The proof involves embedding certain fields inside the p-adic numbers for some prime , and using properties of zeros of power series over (Strassman's theorem).; 0