【摘要】：數(shù)論中的指數(shù)和,Kloosterman和,Guass和,Ramanujan和等和式都有緊密的聯(lián)系.近年來,很多學者深入的研究了這些問題,并且獲得了很多優(yōu)秀的研究成果.本文運用簡化剩余系,三角和,Dirichlet特征的正交性,Ramanujan和等性質以及學者研究所利用的方法,對己有的各種指數(shù)和進行推廣.研究結果如下:1.對于正整數(shù)q(q≥ 3),m,n,kk,s,其中n滿足(n,q)= 1,研究了(?)的均值,并且得到了 一個精確的計算公式.2.設t為正整數(shù),k1,k2,…,kt及m1,m2,…,mt,n均為正整數(shù)且p為素數(shù),設q2為整數(shù),且滿足(m2,q)=…=(mt,q)=(n,q)= 1.令L =k1 + k2+…+kt,多項式φ(x)=m1xk1+ m2xk2+…+mtxkt,研究了(?)的均值,并且分別給出了當(k1,q)= 1及k1|k2,k1|k3,…,k1|kt,正整數(shù)n滿足(n,q)= 1,或(k1,qφ(q))=1,正整數(shù)n滿足(n,p)= 1時的恒等式.3.設p,m,k,l,α是正整數(shù)且p是素數(shù),那么對正整數(shù)n且(n,p)= 1,研究了(?)并獲得了一個等式.
[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，

本文編號：2333748