关于一些指数和的均值研究
发布时间：2018-11-15 15:57
【摘要】：数论中的指数和,Kloosterman和,Guass和,Ramanujan和等和式都有紧密的联系.近年来,很多学者深入的研究了这些问题,并且获得了很多优秀的研究成果.本文运用简化剩余系,三角和,Dirichlet特征的正交性,Ramanujan和等性质以及学者研究所利用的方法,对己有的各种指数和进行推广.研究结果如下:1.对于正整数q(q≥ 3),m,n,kk,s,其中n满足(n,q)= 1,研究了(?)的均值,并且得到了 一个精确的计算公式.2.设t为正整数,k1,k2,…,kt及m1,m2,…,mt,n均为正整数且p为素数,设q2为整数,且满足(m2,q)=…=(mt,q)=(n,q)= 1.令L =k1 + k2+…+kt,多项式φ(x)=m1xk1+ m2xk2+…+mtxkt,研究了(?)的均值,并且分别给出了当(k1,q)= 1及k1|k2,k1|k3,…,k1|kt,正整数n满足(n,q)= 1,或(k1,qφ(q))=1,正整数n满足(n,p)= 1时的恒等式.3.设p,m,k,l,α是正整数且p是素数,那么对正整数n且(n,p)= 1,研究了(?)并获得了一个等式.
[Abstract]:In number theory, the sum of exponents, Kloosterman and, Guass and, Ramanujan and sum are closely related. In recent years, many scholars have studied these problems in depth, and obtained a lot of excellent research results. In this paper, by using the orthogonality, Ramanujan sum and other properties of simplified residue systems, trigonometric sums, Dirichlet features and the methods used by scholars, we generalize the existing exponential sums. The results are as follows: 1. For a positive integer q (q 鈮，
本文编号：2333748
[Abstract]:In number theory, the sum of exponents, Kloosterman and, Guass and, Ramanujan and sum are closely related. In recent years, many scholars have studied these problems in depth, and obtained a lot of excellent research results. In this paper, by using the orthogonality, Ramanujan sum and other properties of simplified residue systems, trigonometric sums, Dirichlet features and the methods used by scholars, we generalize the existing exponential sums. The results are as follows: 1. For a positive integer q (q 鈮，
本文编号：2333748
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