Traces of CM values of modular functions

被引:66
作者
Bruinier, JH
Funke, J
机构
[1] Univ Cologne, Inst Math, D-50931 Cologne, Germany
[2] New Mexico State Univ, Dept Math Sci, Las Cruces, NM 88001 USA
来源
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2006年 / 594卷
关键词
D O I
10.1515/CRELLE.2006.034
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also study the theta lift for the weight 0 Eisenstein series for SL2(Z) and realize a certain generating series of arithmetic intersection numbers as the derivative of Zagier's Eisenstein series of weight 3/2. This recovers a result of Kudla, Rapoport and Yang.
引用
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页码:1 / 33
页数:33
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