Roelof Bruggeman

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into the structure of L2(Γ\G), with Γ = PSL2(Z) and G = PSL2(R). It is shown that there exists a Γ -automorphic function on G, whose value at the unit element is closely related to Z2(g), and whose spectral decomposition in L 2(Γ\G) gives rise to that of Z2(g). This amounts to an alternative and direct proof of the explicit formula for Z2(g) that was(More)
A. The eigenfunctions with eigenvalues 1 or −1 of the transfer operator of Mayer are in bijective correspondence with the eigenfunctions with eigenvalue 1 of a transfer operator connected to the nearest integer continued fraction algorithm. This is shown by relating these eigenspaces of these operators to cohomology groups for the modular group with(More)
The aim of the present article is to exhibit a new proof of the explicit formula for the fourth moment of the Riemann zeta-function that was established by the second named author a decade ago. Our proof is new, particularly in that it dispenses altogether with the spectral theory of sums of Kloosterman sums that played a predominant rôle in the former(More)
We write x = Re z and y = Im z for z ∈ H, and use the Whittaker function W·,·( · ), see, e.g., [12], 1.7. One can express W0,· in terms of a modified Bessel function: W0,μ(y) = √ y/πKμ(y/2). These Maass forms occur as eigenfunctions in the spectral decomposition of the Laplacian in L ( Γmod\H, dxdy y2 ) , with Γmod := PSL2(Z). The eigenvalue is s (1− s).(More)
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