Regularized theta lifts for orthogonal groups over totally real fields

被引：13

作者：

Bruinier, Jan Hendrik ^{[1
]}

机构：

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

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2012年 / 672卷

关键词：

KOHNEN-ZAGIER THEOREM; AUTOMORPHIC-FORMS; EISENSTEIN SERIES; HEEGNER POINTS; DERIVATIVES; ALGEBRAS; CYCLES;

D O I：

10.1515/CRELLE.2011.163

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a regularized theta lift from SL2 to orthogonal groups over totally real fields. It takes harmonic 'Whittaker forms' to automorphic Green functions and weakly holomorphic Whittaker forms to meromorphic modular forms on orthogonal groups with zeros and poles supported on special divisors, generalizing Borcherds' work on automorphic products. To prove our results, we use the spectral expansion of the lift and study its relationship with the cohomological theta lift of Kudla and Millson.

引用

页码：177 / 222

页数：46

共 49 条

[1]

Abramowitz M., 1984, Pocketbook of mathematical functions

[2] Cubic surfaces and Borcherds products [J].

Allcock, D ;

Freitag, E .

COMMENTARII MATHEMATICI HELVETICI, 2002, 77 (02) :270-296

[3]

[Anonymous], 1954, TABLES INTEGRAL TRAN

[4]

[Anonymous], 1991, Discrete subgroups of semisimple Lie groups

[5] Automorphic forms with singularities on Grassmannians [J].

Borcherds, RE .

INVENTIONES MATHEMATICAE, 1998, 132 (03) :491-562

[6] The Gross-Kohnen-Zagier theorem in higher dimensions [J].

Borcherds, RE .

DUKE MATHEMATICAL JOURNAL, 1999, 97 (02) :219-233

[7]

Bruinier J., 2002, LECT NOTES MATH, V1780

[8]

Bruinier J.H., 2011, ADV LECT MATH ALM, P1

[9] Borcherds products and arithmetic intersection theory on Hilbert modular surfaces [J].

Bruinier, Jan H. ;

Burgos Gil, Jose I. ;

Kuehn, Ulf .

DUKE MATHEMATICAL JOURNAL, 2007, 139 (01) :1-88

[10] Faltings heights of CM cycles and derivatives of L-functions [J].

Bruinier, Jan Hendrik ;

Yang, Tonghai .

INVENTIONES MATHEMATICAE, 2009, 177 (03) :631-681

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