Average values of modular L-series via the relative trace formula
| dc.creator | Ramakrishnan, Dinakar | |
| dc.creator | Rogawski, Jonathan | |
| dc.date | 2005-10-06 | |
| dc.date | 2006-09-16 | |
| dc.date.accessioned | 2026-07-07T06:47:10Z | |
| dc.date.available | 2026-07-07T06:47:10Z | |
| dc.description | First we reprove, using representation theory and the relative trace formula of Jacquet, an average value result of Duke for modular L-series at the critical center. We also establish a refinement. To be precise, the L-value which appears is L(1/2, f)L(1/2,f,χ) (divided by the Petersson norm of f), and the average is over newforms f of prime level N and coefficients a_p(f), with χbeing an odd quadratic Dirichlet character of conductor -D and associated quadratic field K. For any prime p not dividing ND, the asymptotic as N goes to infinity is governed by a measure μ_p, which is the Plancherel measure at p when χ(p)=-1, but is new if χ(p)=1; as p goes to infinity both measures approach the Sato-Tate measure. A particular consequence of our refinement is that for any non-empty interval J in [-2,2], there are infinitely many primes N, which are inert in K, such that for some f of level N, a_p(f) is in J and L(1/2, f)L(1/2,f,χ) is non-zero. | |
| dc.identifier | https://arxiv.org/abs/math/0510113 | |
| dc.identifier | http://arxiv.org/abs/math/0510113 | |
| dc.identifier | Pure and Applied Mathematics Quarterly 1 (4), Special Issue in Memory of Armand Borel, Part 3 of 3 (2006), 701-735 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103570 | |
| dc.subject | Number Theory | |
| dc.title | Average values of modular L-series via the relative trace formula | |
| dc.type | text |