On class number relations, intersections, and GL(2)-tale over the function field side

2020/12/16 by Guo, Jia-Wei, Fu‐Tsun Wei, Wei, Fu-Tsun
Mathematics · #11F27 #11F30 #11G18 #11R29 #11R58 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.08728

openalex publication_date 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Heegner points and derivatives ofL-series. II

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