Genus Zero Modular Functions
| dc.creator | Lian, Bong H. | |
| dc.creator | Wiczer, Joshua L. | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T07:32:43Z | |
| dc.date.available | 2026-07-07T07:32:43Z | |
| dc.description | This project was sponsored through the Schiff Fellowship program of Brandeis University. This project involved using the power series method to construct a third order nonlinear ordinary differential equation, a Schwarzian equation, for each of the "genus zero" modular functions, described in the Conway-Norton paper. We first use the Borcherd recursion formuli to generate, in each case, a modular function up to whatever degree we desire, and then use the fact that there is a Schwarzian equation, determined by a single rational function we call a Q-value. By similar power series methods, we compute the coefficients of our rational function, and hence have all the necessary data to create a Schwarzian differential equation for each modular function. This equation can, in turn, be used to recover the modular function itself. | |
| dc.description | 22 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0611291 | |
| dc.identifier | http://arxiv.org/abs/math/0611291 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119210 | |
| dc.subject | Number Theory | |
| dc.subject | 11F03 | |
| dc.title | Genus Zero Modular Functions | |
| dc.type | text |