Liftings and Borcherds products
This chapter serves as a brief introduction to the theory of theta-liftings with the main focus on Borcherds’ singular theta-lift and the construction of Borcherds products. Thus, after a few initial examples for liftings, we proceed to develop the tools needed to understand how the Borcherds lift w...
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| Format: | Chapter/Article Conference Paper |
| Language: | English |
| Published: |
16 October 2017
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| In: |
L-functions and Automorphic Forms
Year: 2017, Pages: 333-366 |
| DOI: | 10.1007/978-3-319-69712-3_19 |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1007/978-3-319-69712-3_19 Verlag, Volltext: https://link.springer.com/chapter/10.1007/978-3-319-69712-3_19 
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| Author Notes: | Eric Hofmann |
MARC
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| 520 | |a This chapter serves as a brief introduction to the theory of theta-liftings with the main focus on Borcherds’ singular theta-lift and the construction of Borcherds products. Thus, after a few initial examples for liftings, we proceed to develop the tools needed to understand how the Borcherds lift works. Namely, we go through the construction of symmetric domains for orthogonal groups, introduce vector-valued modular forms and explain the definition of the Siegel theta-function. Then, we give a detailed treatment of the regularization recipe for the theta-integral and of the proof for the key properties of the additive lift: the location and type of its singularities. Finally, in the closing section, we sketch how to obtain a multiplicative lifting and the Borcherds’ products. | ||
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