科研之友
微信
新浪微博
Facebook
分享链接
摘要
It is a well known fact that, if p is an odd prime, then the pth-elementary cyclotomic polynomial Phi(p)(x) has an associated p-Eisenstein polynomial Phi(p)(x). We extend this construction and show that, every order one elementary cyclotomic polynomial Phi 2(s)p(t) (x) has an associated p-Eisenstein polynomial Phi 2(s)p(t)(x). In addition, for each Phi 2(s)p(t) (X), we investigate the divisibility (with respect to the prime p) of the coefficients of Phi 2(s)p(t)(x). We also establish analogous results for order one Carlitz cyclotomic polynomials over F-q[T].
