Polynomial moments with a weighted zeta square measure on the critical line
Polynomial moments with a weighted zeta square measure on the critical line
We prove closed-form identities for the sequence of moments $\int t^{2n}|\Gamma (s)\zeta (s)|^2\,dt$ on the whole critical line $s=1/2+it$. They are finite sums involving binomial coefficients, Bernoulli numbers, Stirling numbers and $\pi $, in particular