On holomorphic projection for symplectic groups
We construct certain Casimir operators and study the spectral properties of their resolvents on L2(Γ\Sp2(R)). We define non-holomorphic multi-variable Poincaré series of exponential type for symplectic groups and continue them analytically in case of genus two for the small weight four using the ab...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 2018
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| In: |
Journal of number theory
Year: 2018, Volume: 182, Pages: 131-178 |
| ISSN: | 1096-1658 |
| DOI: | 10.1016/j.jnt.2017.06.005 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1016/j.jnt.2017.06.005 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0022314X17302329 
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| Author Notes: | Kathrin Maurischat |
| Summary: | We construct certain Casimir operators and study the spectral properties of their resolvents on L2(Γ\Sp2(R)). We define non-holomorphic multi-variable Poincaré series of exponential type for symplectic groups and continue them analytically in case of genus two for the small weight four using the above resolvents. We apply our results to describe the holomorphic projection to the weight four holomorphic discrete series in terms of Fourier coefficients by using Sturm's operator. This paper is a study of a prototype for symplectic groups and special orthogonal groups. |
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| Item Description: | Available online: 18 July 2017 Gesehen am 19.03.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1096-1658 |
| DOI: | 10.1016/j.jnt.2017.06.005 |