Error term in the prime geodesic theorem
Event details
| Date | 28.03.2017 |
| Hour | 14:15 › 15:15 |
| Speaker | João Guerreiro (Max Planck Institute for Mathematics - Bonn) |
| Location |
MA A1 10
|
| Category | Conferences - Seminars |
Abstract: Closed geodesics on the surface $\text{PSL}_2(\mathbb{Z}) \backslash \mathbb{H}$, where $\mathbb{H}$ is the upper half plane, satisfy an asymptotic law that is very similar to the one describing the distribution of prime numbers. Moreover, the error term in this asymptotic law is related to the spectrum of the Laplace operator, which is also the set of zeros of the Selberg zeta function. In this talk, I will exploit the connection between closed geodesics and Maaß cusp forms to estimate the error term in the prime geodesic theorem, giving a bound for its mean square. This is joint work with Giacomo Cherubini.
Practical information
- Informed public
- Free
Organizer
- Philippe Michel
Contact
- Monique Kiener