The correlation between multiplicities of closed geodesics on the modular surface

Mathematics – Number Theory

Scientific paper

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17 pages

Scientific paper

10.1007/s002201000574

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.

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