Harmonic Maass forms associated to real quadratic fields

被引：6

作者：

Charollois, Pierre ^{[1
]}

Li, Yingkun ^{[2
]}

机构：

[1] Sorbonne Univ, Inst Math Jussieu, PRG, CNRS, 4 Pl Jussieu, F-75005 Paris, France

[2] Tech Univ Darmstadt, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2020年 / 22卷 / 04期

关键词：

Harmonic Maass form; Fourier coefficients; real quadratic field; theta lift; MODULAR-FORMS; FALTINGS HEIGHTS;

D O I：

10.4171/JEMS/941

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we explicitly construct harmonic Maass forms that map to the holomorphic weight 1 theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this construction, we give precise arithmetic information contained in the Fourier coefficients of the holomorphic part of the harmonic Maass form, establishing the main part of a conjecture of the second author.

引用

页码：1115 / 1148

页数：34

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