Poincaré series for SO(n, 1)

Jian Shu Li, I. Piatetski-Shapiro, P. Sarnak

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)231-237
Number of pages7
JournalProceedings of the Indian Academy of Sciences - Mathematical Sciences
Issue number1-3
StatePublished - Dec 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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


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