Polynomial Moments with a weighted Zeta Square measure on the critical line

Sébastien Darses, Erwan Hillion

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,…