On class number relations and intersections over function fields

  • Jia-Wei Guo

    Department of Mathematics, National Taiwan University, Taipei, Taiwan
  • Fu-Tsun Wei

    Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
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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