不完全区间上类特征和的混合均值

On the hybrid mean value of a sum analogous to character sum over quarter interval

研究不完全区间上类特征和的两类混合均值的分布性质.利用特征和的性质将其转化为Gauss和与Dirichlet L-函数的求和式,同时结合原特征的性质与L-函数的均值定理,得到几个较强的渐近公式.

Two kinds of hybrid mean value of a sum analogous to character sums over quarter interval are studied .By transforming the sum into a sum involving Gauss sums and Dirichlet L-functions ,then using the properties of primitive character and estimates of Dirichlet L-functions ,some sharper asymptotic for-mulae of them are obtained .