L-functions of degree d can be parametrized, in two different ways, by points with an attached multiplicity in (d-1)-dimensional Euclidean space. One approach separates the L-functions according to the shape of the Gamma-factors in the functional equation, equivalently, according to the infinity type of the underlying automorphic representation. The other approach combines all the L-functions of a given degree into a single picture in which the points, to leading order, are uniformly dense. We will describe these classifications and provide examples of several ‘landscapes’ in the L-function world.
This video (which is better viewed on Panopto, here) was produced by ICERM at Brown University, as part of the conference LMFDB, Computation and Number Theory.
