Abstract
We determine the variance for the fluctuations of the arithmetic measures obtained by collecting all closed geodesics on the modular surface with the same discriminant and ordering them by the latter. This arithmetic variance differs by subtle factors from the variance that one gets when considering individual closed geodesics when ordered by their length. The arithmetic variance is the same one that appears in the fluctuations of measures associated with quantum states on the modular surface.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 271-309 |
| Number of pages | 39 |
| Journal | Journal of Modern Dynamics |
| Volume | 3 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2009 |
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Applied Mathematics
Keywords
- Arithmetic variance
- Closed geodesics
- Modular surface