On the distribution of the zeros of the Riemann zeta function in short intervals
Let \(s(t)=(1/\pi)\arg \zeta (+it)\). Assuming the Riemann Hypothesis the author obtains an asymptotic formula for \(\int^{T}_{0}(s(t+\Delta)- s(t))^ 2dt\), where \(\Delta =o(1)\). The method is based on \textit{D. A. Goldston}'s paper [J. Number Theory 27, 149-177 (1987; Zbl 0618.10037)] and the result refines a previous result of the author [Bull. Am. Math. Soc. 81, 139-142 (1975; Zbl 0297.10026)].
scientific article; zbMATH DE number 4156559
scientific article