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Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth
We investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that expresses the coefficients of all such terms as resid...
Autores principales: | , , , |
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Lenguaje: | eng |
Publicado: |
2019
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Materias: | |
Acceso en línea: | http://cds.cern.ch/record/2697244 |
_version_ | 1780964208205103104 |
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author | Belin, Alexandre Castro, Alejandra Keller, Christoph A. Mühlmann, Beatrix J. |
author_facet | Belin, Alexandre Castro, Alejandra Keller, Christoph A. Mühlmann, Beatrix J. |
author_sort | Belin, Alexandre |
collection | CERN |
description | We investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that expresses the coefficients of all such terms as residues. We find that there are two types of weak Jacobi forms, leading to two different growth behaviors: the more common type leads to fast, exponential growth, whereas a second type leads to slower growth, akin to the growth seen in ratios of theta functions. We give a simple criterion to distinguish between the two types, and give a simple closed form expression for the coefficients in the slow growing case. In a companion article [1], we provide physical applications of these results to symmetric product orbifolds and holography. |
id | cern-2697244 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2019 |
record_format | invenio |
spelling | cern-26972442022-05-10T02:19:05Zhttp://cds.cern.ch/record/2697244engBelin, AlexandreCastro, AlejandraKeller, Christoph A.Mühlmann, Beatrix J.Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growthmath.NTMathematical Physics and Mathematicshep-thParticle Physics - TheoryWe investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that expresses the coefficients of all such terms as residues. We find that there are two types of weak Jacobi forms, leading to two different growth behaviors: the more common type leads to fast, exponential growth, whereas a second type leads to slower growth, akin to the growth seen in ratios of theta functions. We give a simple criterion to distinguish between the two types, and give a simple closed form expression for the coefficients in the slow growing case. In a companion article [1], we provide physical applications of these results to symmetric product orbifolds and holography.arXiv:1910.05353CERN-TH-2019-163oai:cds.cern.ch:26972442019 |
spellingShingle | math.NT Mathematical Physics and Mathematics hep-th Particle Physics - Theory Belin, Alexandre Castro, Alejandra Keller, Christoph A. Mühlmann, Beatrix J. Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth |
title | Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth |
title_full | Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth |
title_fullStr | Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth |
title_full_unstemmed | Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth |
title_short | Siegel Paramodular Forms from Exponential Lifts: Slow versus Fast Growth |
title_sort | siegel paramodular forms from exponential lifts: slow versus fast growth |
topic | math.NT Mathematical Physics and Mathematics hep-th Particle Physics - Theory |
url | http://cds.cern.ch/record/2697244 |
work_keys_str_mv | AT belinalexandre siegelparamodularformsfromexponentialliftsslowversusfastgrowth AT castroalejandra siegelparamodularformsfromexponentialliftsslowversusfastgrowth AT kellerchristopha siegelparamodularformsfromexponentialliftsslowversusfastgrowth AT muhlmannbeatrixj siegelparamodularformsfromexponentialliftsslowversusfastgrowth |