High moments of the Estermann function
Event details
| Date | 22.02.2017 |
| Hour | 14:15 › 15:15 |
| Speaker | Sandro Bettin (Università di Genova) |
| Location |
CH B3 31
|
| Category | Conferences - Seminars |
Abstract: For a rational number h/k, the Estermann function is defined as the Dirichlet series D(s,h/k)=\sum_{n\geq1} d(n) e^{2\pi n h/k} /n^s for \Re(s)>1 and by meromorphic continuation in the rest of the complex plane. We will show how to compute all moments of the Estermann function at the central point s=1/2 when averaging over h modulo k as k goes to infinity among primes. In doing so we are also led to the computation of the asymptotic with power saving error term for the number of points in the projective variety x_0y_0+...+x_m y_m=0.
Practical information
- Informed public
- Free
Organizer
- Philippe Michel
Contact
- Monique Kiener