Holomorphic Siegel Modular Forms Associated to SO(n, 1).
Let be a Hecke–Maass cusp form of eigenvalue and square-free level . Normalize the hyperbolic measure such that and the form such that . It is shown that for all . This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.
For a cocompact group of we fix a real non-zero harmonic -form . We study the asymptotics of the hyperbolic lattice-counting problem for under restrictions imposed by the modular symbols . We prove that the normalized values of the modular symbols, when ordered according to this counting, have a Gaussian distribution.