A Spanning Set for the space of Super Cusp forms

Details A Spanning Set for the space of Super Cusp forms A Spanning Set for the space of Super Cusp forms

2008-07-07

arxiv.org/abs/0807.0988v5

Mathematics

Complex Variables

46 pages, 2 figures. Minor changes in replacement

Scientific paper

Aim of this article is the construction of a spanning set for the space of super cusp forms on a complex bounded symmetric super domain B of rank 1 with respect to a lattice. The main ingredients are a generalization of the Anosov closing lemma for partially hyperbolic diffeomorphisms and an unbounded realization of B, in particular Fourier decomposition at the cusps mapped to infinity via a partial Cayley transformation. The elements of the spanning set are in finite-to-one correspondence with closed geodesics, the number of elements corresponding to a geodesic growing linearly with its length.

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