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.
Original language | English (US) |
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Pages (from-to) | 231-237 |
Number of pages | 7 |
Journal | Proceedings of the Indian Academy of Sciences - Mathematical Sciences |
Volume | 97 |
Issue number | 1-3 |
DOIs | |
State | Published - Dec 1987 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Lobachevsky space
- Poincaré series
- Selberg-Kloosterman zeta function
- non-uniform lattices