Andrew Sutherland, May 28, 2020

Title: Computing L-functions of modular curves

Abstract: I will present a new algorithm for counting points on modular curves over finite fields that is faster (and more general) than previous methods, building on ideas of Zywina that were exploited in our prior joint work. A key feature of this algorithm is that it does not require a model of the curve. I will then describe how this can be used to compute the L-function of the curve and an upper bound on the analytic rank of its Jacobian that is provably tight if it is less than 2.