On class number relations and intersections over function fields

Abstract: In this talk, we shall discuss a function field analogue of the Hirzebrush-Zagier class number formula. More precisely, we establish a connection between class numbers of "imaginary" quadratic function fields and the corresponding intersections of "Heegner-type" divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is the theta series associated to anisotropic quadratic spaces of dimension 4. The connection directly comes from two different expressions of the Fourier coefficients of the theta series, which can be viewed as a geometric Siegel-Weil formula in this particular case. This is a joint work with Jia-Wei Guo.

number theory

Audience: researchers in the topic

Number Theory Online Conference 2020