  An explicit product representation is proved for the correlation function of
the multiplicities of closed geodesics on the modular surface. This makes
rigorous part of the investigation of Bogomolny, Leyvraz and Schmit on the
correlation of the eigenvalues of the Laplacian on the modular surface. The
result can also be seen as a (rigorously proved) analogue of the
Hardy-Littlewood twin prime conjecture.
