The Fourier-Jacobi expansion of the singular theta lift
Recently, Funke and Hofmann constructed a singular theta lift of Borcherds type for the dual reductive pair \(U(1,1)\times U(p,q)\), \(p,q\geq 1\), the input functions of which are harmonic weak Maass forms of weight \(k= 2-p-q\). In the present paper, we give an explicit evaluation of the Fourier-J...
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| description | Recently, Funke and Hofmann constructed a singular theta lift of Borcherds type for the dual reductive pair \(U(1,1)\times U(p,q)\), \(p,q\geq 1\), the input functions of which are harmonic weak Maass forms of weight \(k= 2-p-q\). In the present paper, we give an explicit evaluation of the Fourier-Jacobi expansion of the lift. For this purpose, we adapt a method introduced by Kudla in his paper 'Another product for a Borcherds form'. As an application, in the case \(U(p,1)\) we recover a new infinite product expansion associated to a Borcherds form, analogous to the case \(O(p,2)\) treated by Kudla. |
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In the present paper, we give an explicit evaluation of the Fourier-Jacobi expansion of the lift. For this purpose, we adapt a method introduced by Kudla in his paper 'Another product for a Borcherds form'. As an application, in the case \(U(p,1)\) we recover a new infinite product expansion associated to a Borcherds form, analogous to the case \(O(p,2)\) treated by Kudla.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Harmonic functions</subject><ispartof>arXiv.org, 2022-12</ispartof><rights>2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). 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| title | The Fourier-Jacobi expansion of the singular theta lift |
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