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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...

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Detalles Bibliográficos
Autores principales: Belin, Alexandre, Castro, Alejandra, Keller, Christoph A., Mühlmann, Beatrix J.
Lenguaje:eng
Publicado: 2019
Materias:
Acceso en línea:http://cds.cern.ch/record/2697244
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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.
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2019
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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
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AT castroalejandra siegelparamodularformsfromexponentialliftsslowversusfastgrowth
AT kellerchristopha siegelparamodularformsfromexponentialliftsslowversusfastgrowth
AT muhlmannbeatrixj siegelparamodularformsfromexponentialliftsslowversusfastgrowth