分圆多项式及其变形的一点注记  

A Note on Cyclotomic Polynomial and Their Variants

作　　者：王曼 赵正俊 WANG Man;ZHAO Zhengjun(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2021年第3期22-25,共4页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11971382)。

摘　　要：分圆多项式的性质在密码学领域具有重要的应用,研究分圆多项式的性质具有重要的理论意义。就分圆多项式在整体函数域中的模拟及由映射的复合所诱导的动力分圆多项式进行研究。结合动力系统的思想,利用数论的方法,给出了与动力分圆多项式相关的若干性质的证明。经典分圆理论在不同的背景下具有很多相似之处,这对丰富分圆理论具有重要的意义。The properties of cyclotomic polynomials have important applications in the field of cryptography. It is of great theoretical significance to study the properties of cyclotomic polynomials. This paper mainly introduces the simulation of classical cyclotomic polynomials in the global function field and the dynamic cyclotomic polynomials induced by the composition of maps. Combined with the idea of dynamic system, some properties related to dynamic cyclotomic polynomials are proved by using the method of number theory. The classical cyclotomic theory has many similarities in different backgrounds,which is of great significance to enrich the cyclotomic theory.

关 键 词：分圆多项式 Carlitz模 Drinfeld模 动力分圆多项式 

分 类 号：O156[理学—数学]