• P Sarnak

      Articles written in Proceedings – Mathematical Sciences

    • Poincaré series forSO(n, 1)

      Jian-Shu Li I Piatetski-Shapiro P Sarnak

      More Details Abstract Fulltext PDF

      A theory of Poincaré series is developed for Lobachevsky space of arbitrary dimension. For a general non-uniform lattice a Selberg-Kloosterman zeta function is introduced. It has meromorphic continuation to the plane with poles at the corresponding automorphic spectrum. When the lattice is a unit group of a rational quadratic form, the Selberg-Kloosterman zeta function is computed explicitly in terms of exponential sums. In this way a non-trivial Ramanujan-like bound analogous to “Selberg’s 3/16 bound” is proved in general.

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