On class number relations, intersections, and GL(2)-tale over the function field side
Number Theory
2021-03-31 v2
Abstract
The aim of this paper is to study class number relations over function fields and the intersections of Hirzebruch-Zagier type divisors on the Drinfeld-Stuhler modular surfaces. The main bridge is a particular "harmonic" theta series with nebentypus. Using the strong approximation theorem, the Fourier coefficients of this series are expressed in two ways; one comes from modified Hurwitz class numbers and another gives the intersection numbers in question. An elaboration of this approach enables us to interpret these class numbers as a "mass sum" over the CM points on the Drinfeld-Stuhler modular curves, and even realize the generating function as a metaplectic automorphic form.
Keywords
Cite
@article{arxiv.2012.08728,
title = {On class number relations, intersections, and GL(2)-tale over the function field side},
author = {Jia-Wei Guo and Fu-Tsun Wei},
journal= {arXiv preprint arXiv:2012.08728},
year = {2021}
}