On a hybrid mean value of the character sums over short intervals
Let \(B(\chi)\) be the constant in the zero expansion of logarithmic differentiation of the \(L(s,\chi)\), \(S(q/4,\chi)\) be the character sum over \([1,q/4)\). In this paper,the following result is obtained. Theorem. Let \(q\geq 5\), then \[ \sideset\and {^*}\to\sum\limits_{\chi \bmod q} |B(\chi)S(q/4,\chi)|^{2}=CqJ(q)+O(q^{1+\varepsilon}), \] where \(J(q)\) is the number of all primitive characters modulo \(q\). The proofs use the mean value theorems of the \(L\)-functions.
scientific article; zbMATH DE number 5654313
scientific article