Taking t at random, uniformly from [0,T], we consider the kth moment, with respect to t, of random variable corresponding 2?th moment ?(1/2+ix) over interval x?(t,t+1], where ?(s) is Riemann zeta function. We call these ‘moments moments’ function, and present a conjecture for their asymptotics, when T??, integer k,?. This motivated by comparisons results moments characteristic polynomials unita...