We prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range. In fact it is close to having a Poisson behavior. This fact was discovered numerically by Schmit, Bogomolny, Georgeot and Giannoni. It has its origin in the high degeneracy of the length spectrum, first observed by Selberg.
|Original language||English (US)|
|Number of pages||14|
|Journal||Communications In Mathematical Physics|
|State||Published - Mar 1994|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics