Sums of Hecke eigenvalues over quadratic polynomials
| dc.creator | Blomer, Valentin | |
| dc.date | 2008-03-30 | |
| dc.date.accessioned | 2026-07-07T09:29:21Z | |
| dc.date.available | 2026-07-07T09:29:21Z | |
| dc.description | Let f(z) = sum_n a(n) n^{(k-1)/2} e(nz) be a cusp form for Gamma_0(N), character chi and weight k geq 4. Let q(x) = x^2 + sx + t be a polynomial with integral coefficients. It is shown that sum_{n \leq X} a(q(n)) = cX + O(X^{6/7+eps}) for some constant c depending on f and q. The constant vanishes in many cases, for example if k is even. On the way a Kuznetsov formula for half-integral weight and entries having different sign is derived. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0803.4301 | |
| dc.identifier | http://arxiv.org/abs/0803.4301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157751 | |
| dc.subject | Number Theory | |
| dc.subject | 11F30, 11F37, 11N37 | |
| dc.title | Sums of Hecke eigenvalues over quadratic polynomials | |
| dc.type | text |