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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/097/01-03/0231-0237

    • Keywords

       

      Poincaré series; Lobachevsky space; Selberg-Kloosterman zeta function; non-uniform lattices

    • Abstract

       

      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.

    • Author Affiliations

       

      Jian-Shu Li1 I Piatetski-Shapiro P Sarnak2

      1. Massachusetts Institute of Technology, Cambridge, Massachusetts - 02139, USA
      2. The Institute for Advanced Studies, The Hebrew University of Jerusalem, Givat Ram, Jerusalem - 91904, Israel
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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