Traces of CM Values and Geodesic Cycle Integrals of Modular Functions

Traces of CM Values and Geodesic Cycle Integrals of Modular Functions

Explore the fascinating world of generating series of traces of CM values and geodesic cycle integrals of modular functions in this 46-minute lecture by Claudia Alfes from the Hausdorff Center for Mathematics. Begin with an introduction to modular forms and harmonic Maass forms, then delve into the theory of theta lifts, which provides a conceptual framework for these generating series. Discover practical applications of this theory, including its use in obtaining results on the vanishing of the central derivative of L-series of elliptic curves and rationality results for cycle integrals of certain meromorphic functions.