A Note on the Mean Value of Numbers of the Solutions of x~α=1(mod n)  

作　　者：Xiu Yuan YU 

机构地区：[1]Department of Mathematics,Hangzhou Teachers' College [2]Department of Mathematics,Quzhou College

出　　处：《Acta Mathematica Sinica,English Series》2004年第6期1095-1102,共8页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(No.19971024);Zhejiang Provincial Natural Science Foundation of China(No.199047)

摘　　要：Let T=T(p,q,α) be the number of solutions of the congruence x~α≡1 (rood p^nq~θ).Let A and B be sets of primes satisfying x_1<p≤x_2 and y_1<q≤y_2,respectively.A mean value estimation of (?)∑_(p∈A)∑_(q∈B) logT (p,q,α) is given.Let T=T(p,q,α) be the number of solutions of the congruence x~α≡1 (rood p^nq~θ).Let A and B be sets of primes satisfying x_1<p≤x_2 and y_1<q≤y_2,respectively.A mean value estimation of (?)∑_(p∈A)∑_(q∈B) logT (p,q,α) is given.

关 键 词：CONGRUENCE Number of solutions Mean value 

分 类 号：O156[理学—数学]