Moments of L-functions and a technique of Sound and Young
Event details
| Date | 02.10.2013 |
| Hour | 15:00 › 16:00 |
| Speaker | Ian Petrow (EPFL) |
| Location | |
| Category | Conferences - Seminars |
Abstrait: Let f be a classical holomorphic Hecke cusp form of even weight, odd level and trivial central character. Consider the family of L-functions given by the quadratic twists L(s,f \otimes \chi_K), where \chi_K is the character associated with the quadratic field K. A classical method to study the these L-functions is to estimate the k-th moment of the central values L(1/2, f \otimes \chi_K) or L'(1/2, f \otimes \chi_K) over the family of twists. Very little is know rigorously about this problem, although random matrix theory provides good conjectures. When k=1 it is sufficient to use the trace formula (Poisson summation) to obtain an asymptotic estimate, but already when k=2 the trace formula becomes an involution, and something more is needed. I will discuss a technique of Soundararajan and Young to get around this involutivity and its application (assuming GRH) to obtain asymptotic estimates for the 2nd moment of both L(1/2, f \otimes \chi_K) and L'(1/2,f\otimes \chi_K).
Practical information
- Informed public
- Free
Contact
- Monique Kiener