Geodesic
On class number relations and intersections over function fields
Documenta mathematica, Tome 27 (2022), pp. 1321-1368
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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.
DOI : 10.4171/dm/899
Classification : 11F27, 11F30, 11G18, 11R29, 11R58
Mots-clés : function field, class number relation, Hirzebruch-Zagier divisor, Drinfeld-type automorphic form 
@article{10_4171_dm_899,
     author = {Jia-Wei Guo and Fu-Tsun Wei},
     title = {On class number relations and intersections over function fields},
     journal = {Documenta mathematica},
     pages = {1321--1368},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/899},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/899/}
}
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Jia-Wei Guo; Fu-Tsun Wei. On class number relations and intersections over function fields. Documenta mathematica, Tome 27 (2022), pp. 1321-1368. doi: 10.4171/dm/899

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