Real-dihedral harmonic Maass forms and CM-values of Hilbert modular functions

被引：2

作者：

Li, Yingkun ^{[1
]}

机构：

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

来源：

COMPOSITIO MATHEMATICA | 2016年 / 152卷 / 06期

关键词：

harmonic Maass form; antomorphic Green's function; Galois representation; EISENSTEIN SERIES; DERIVATIVES; WEIGHT; S=1; NEWFORMS; CURVES; FIELDS;

D O I：

10.1112/S0010437X15007770

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study real-dihedral harmonic Maass forms and their Fourier coefficients. The main result expresses the values of Hilbert modular forms at twisted CM 0-cycles in terms of these Fourier coefficients. This is a, twisted version of the main theorem in Bruinier and Yang CM-values of Hilbert modular functions, Invent. Math. 163 (2006), 229-2881 and provides evidence that the individual Fourier coefficients are logarithms of algebraic numbers in the appropriate real-quadratic field. From this result and numerical calculations, we formulate an algebraicity conjecture, which is an analogue of Stark's conjecture in the setting of harmonic Maass forms. Also, we give a conjectural description of the primes appearing in CM-values of Hilbert modular functions.

引用

页码：1159 / 1197

页数：39