Period polynomials and explicit formulas for Hecke operators on Γ_0(2)
| dc.creator | Fukuhara, Shinji | |
| dc.creator | Yang, Yifan | |
| dc.date | 2006-08-15 | |
| dc.date | 2007-07-10 | |
| dc.date.accessioned | 2026-07-07T08:14:44Z | |
| dc.date.available | 2026-07-07T08:14:44Z | |
| dc.description | Let S_{w+2}(Γ_0(N)) be the vector space of cusp forms of weight w+2 on the congruence subgroup Γ_0(N). We first determine explicit formulas for period polynomials of elements in S_{w+2}(Γ_0(N)) by means of Bernoulli polynomials. When N=2, from these explicit formulas we obtain new bases for S_{w+2}(Γ_0(2)), and extend the Eichler-Shimura-Manin isomorphism theorem to Γ_0(2). This implies that there are natural correspondences between the spaces of cusp forms on Γ_0(2) and the spaces of period polynomials. Based on these results, we will find explicit form of Hecke operators on S_{w+2}(Γ_0(2)). As an application of our main theorems, we will also give an affirmative answer to a speculation of Imamoglu and Kohnen on a basis of S_{w+2}(Γ_0(2)). | |
| dc.description | AMS-LaTeX, 30 pages, final version, to appear on the Mathematical Proceedings of the Cambridge Philosophical Society | |
| dc.identifier | https://arxiv.org/abs/math/0608372 | |
| dc.identifier | http://arxiv.org/abs/math/0608372 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133236 | |
| dc.subject | Number Theory | |
| dc.subject | 11F25;11F11,11F67 | |
| dc.title | Period polynomials and explicit formulas for Hecke operators on Γ_0(2) | |
| dc.type | text |