利用广义Bernoulli数,Gauss和与Dirichlet L-函数的均值来研究r次剩余及其关于模p的逆之差,并给出与广义Kloosterman和相关的一些混合均值公式.

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions to study the asymp- totic property of the difference between an r-th residue and its inverse modulo p(a prime),and give some interesting hybrid mean value formulae involving the general Kloosterman sums.