Title: On Siegel's problem for G-functions
Speaker: Yichen Qin (秦翊宸)
Time: 2.5 (Thursday), 10:30-11:30
Venue: Room 315, Gewu Building
Abstract: G-functions are special power series of arithmetic nature that solve linear differential equations. A rich source of examples, first observed by Siegel, comes from algebraic substitutions of the classical Gauss hypergeometric series. In this talk, we show that not all G-functions arise in this way, thereby giving a negative answer to Siegel's problem for G-functions, as formulated by Fischler and Rivoal. The main ingredients of the proof are the monodromy computations of hypergeometric local systems due to Beukers and Heckman, as well as results on invariant trace fields of Fuchsian groups. This is a joint work with Javier Fresán and Joshua Lam.
