Mathematics – Number Theory
Scientific paper
2001-04-25
Mathematics
Number Theory
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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