Abstract: Given a global function field of characteristic p > 0 and an elliptic curve over it, one can study its L-function. The L-function of an elliptic curve is an interesting object at the interface of complex analysis and algebra and lead to the famous Birch and Swinnerton-Dyer conjecture.

Moreover, explicitly computing an L-function is a non-trivial task. Naive methods involve point-counting and are inefficient. Therefore, alternatives should be welcome.

In this talk, we will first introduce the necessary background on elliptic curves and L-functions. Then, we will discuss a possible approach to effectively tackle the problem of computing L-functions of elliptic curves over global function fields.