This paper gives a survey of known results concerning the Laplace transform $$ L_k(s) := \int_0^\infty |\zeta(1/2+ ix)|^{ 2k}{ \rm e}^{ -sx}{ \rm d} x \qquad(k \in N, \R s > 0), $$ and the (modified) Mellin transform $$ { \cal Z}_k(s) := \int_1^\infty|\zeta(1/2+ ix)|^{ 2k}x^{ -s}{ \rm d} x\qquad(k\in N), $$ where the integral is absolutely convergent for $\R s \ge c(k) > 1$. Also some new results on these integral transforms of $|\zeta(1/2+ ix)|^{ 2k}$ are given, which have important connections with power moments of the Riemann zeta-function $\zeta(s)$.
Categories: math.NT