Conrey and Ghosh studied the second moment of the Riemann zeta function, evaluated at its local extrema along the critical line, finding the leading order behaviour to be $\frac{ e^2 - 5}{ 2 \pi} T (\log T)^2$. This problem is closely related to a mixed moment of the Riemann zeta function and its derivative. We present a new approach which will uncover the lower order terms for the second moment as a descending chain of powers of logarithms in the asymptotic expansion.
Categories: math.NT