The Laplace transform of the fourth moment of the zeta-function

The Laplace transform of $\mathrm{\mid }\zeta (1\mathrm{/}2+it)\mathrm{\mid }$ is investigated, for which a precise expression is obtained, valid in a certain region in the complex plane. The method of proof is based on complex integration and spectral theory of the non-Euclidean Laplacian.