On class number relations and intersections over function fields
Jia-Wei Guo
Department of Mathematics, National Taiwan University, Taipei, TaiwanFu-Tsun Wei
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
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.
Cite this article
Jia-Wei Guo, Fu-Tsun Wei, On class number relations and intersections over function fields. Doc. Math. 27 (2022), pp. 1321–1368
DOI 10.4171/DM/899