Differential equations satisfied by modular forms and K3 surfaces
| dc.creator | Yang, Yifan | |
| dc.creator | Yui, Noriko | |
| dc.date | 2005-06-28 | |
| dc.date | 2006-08-18 | |
| dc.date.accessioned | 2026-07-07T06:42:32Z | |
| dc.date.available | 2026-07-07T06:42:32Z | |
| dc.description | We study differential equations satisfied by modular forms associated to $Γ_1\timesΓ_2$, where $Γ_i (i=1,2)$ are genus zero subgroups of $SL_2(\mathbf R)$ commensurable with $SL_2(\mathbf Z)$, e.g., $Γ_0(N)$ or $Γ_0(N)^*$. In some examples, these differential equations are realized as the Picard--Fuch differential equations of families of K3 surfaces with large Picard numbers, e.g., $19, 18, 17, 16$. Our method rediscovers some of the Lian--Yau examples of ``modular relations'' involving power series solutions to the second and the third order differential equations of Fuchsian type in [14, 15]. | |
| dc.description | Some revisions are incorporated, in particular, replaced the terminology ''bi-modular'' by ''modular'' | |
| dc.identifier | https://arxiv.org/abs/math/0506576 | |
| dc.identifier | http://arxiv.org/abs/math/0506576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102077 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11F03, 11F11, 14D05, 14J28 | |
| dc.title | Differential equations satisfied by modular forms and K3 surfaces | |
| dc.type | text |