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A Spanning Set for the Space of Super Cusp Forms  
 
  Authors: Roland Knevel,  
  Keywords: Automorphic and cusp forms, super symmetry, semisimple Lie groups, partially hyperbolic flows, unbounded realization of a complex bounded symmetric domain.  
  Date Received: 18/07/08  
  Date Accepted: 09/02/09  
  Subject Codes:

Pri: 11F55; Sec: 32C11

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

The aim of this article is the construction of a spanning set for the space $ sS_k(Gamma)$ of super cusp forms on a complex bounded symmetric super domain $ mathcal{B}$ of rank $ 1$ with respect to a lattice $ Gamma$. The main ingredients are a generalization of the ANOSOV closing lemma for partially hyperbolic diffeomorphisms and an unbounded realization $ mathcal{H}$ of $ mathcal{B}$, in particular FOURIER decomposition at the cusps of the quotient $ Gamma ackslash B$ mapped to $ infty$ via a partial CAYLEY transformation. The elements of the spanning set are in finite-to-one correspondence with closed geodesics of the body $ Gamma ackslash B$ of $ Gamma ackslash mathcal{B}$, the number of elements corresponding to a geodesic growing linearly with its length. ;


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