# My research

Currently, my Ph. D. research is about computational aspects of Drinfeld modular forms. A Drinfeld modular forms is a rigid analytic function defined over the Drinfeld upper half plane $f:\Omega \rightarrow C$ such that

$f\left( \frac{az+b}{cz+d} \right) = (\mathrm{det}\gamma)^{-m}(cz+d)^k f(z)$

where $a,b,c,d\in A = \mathbb{F}_q[T], ~ ad-bc \neq 0$, $k$ and $m$ are two integers. There is also a holomorphic condition at infinity similar to the classical case, that is $f$ must satisfy an expansion of the form

$f(z) = \sum_{n\geq 0} c_n t(z)^n,$ where $t(z)$ is some function playing the role of parameter at infinity.

Computationnally speaking,