Genus Zero Modular Functions

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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.
22 pages, LaTeX

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Number Theory, 11F03

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http://salesiana.dossiersoluciones.com/handle/123456789/119210

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611291
 http://arxiv.org/abs/math/0611291

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arXiv