On the space of slow growing weak Jacobi forms

Christoph A. Keller; Jason M. Quinones

doi:10.1016/j.jnt.2022.02.010

On the space of slow growing weak Jacobi forms

Research output: Contribution to journal › Article › peer-review

Abstract

Weak Jacobi forms of weight 0 and index m can be exponentially lifted to meromorphic Siegel paramodular forms. It was recently observed that the Fourier coefficients of such lifts are then either fast growing or slow growing. In this note we investigate the space of weak Jacobi forms that lead to slow growth. We provide analytic and numerical evidence for the conjecture that there are such slow growing forms for any index m.

Original language	English (US)
Pages (from-to)	730-750
Number of pages	21
Journal	Journal of Number Theory
Volume	240
DOIs	https://doi.org/10.1016/j.jnt.2022.02.010
State	Published - Nov 2022
Externally published	Yes

Keywords

Automorphic forms
Holography
Jacobi forms
Modular forms
Theta series

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2022.02.010

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abstract = "Weak Jacobi forms of weight 0 and index m can be exponentially lifted to meromorphic Siegel paramodular forms. It was recently observed that the Fourier coefficients of such lifts are then either fast growing or slow growing. In this note we investigate the space of weak Jacobi forms that lead to slow growth. We provide analytic and numerical evidence for the conjecture that there are such slow growing forms for any index m.",

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year = "2022",

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language = "English (US)",

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AU - Keller, Christoph A.

AU - Quinones, Jason M.

PY - 2022/11

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N2 - Weak Jacobi forms of weight 0 and index m can be exponentially lifted to meromorphic Siegel paramodular forms. It was recently observed that the Fourier coefficients of such lifts are then either fast growing or slow growing. In this note we investigate the space of weak Jacobi forms that lead to slow growth. We provide analytic and numerical evidence for the conjecture that there are such slow growing forms for any index m.

AB - Weak Jacobi forms of weight 0 and index m can be exponentially lifted to meromorphic Siegel paramodular forms. It was recently observed that the Fourier coefficients of such lifts are then either fast growing or slow growing. In this note we investigate the space of weak Jacobi forms that lead to slow growth. We provide analytic and numerical evidence for the conjecture that there are such slow growing forms for any index m.

KW - Automorphic forms

KW - Holography

KW - Jacobi forms

KW - Modular forms

KW - Theta series

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

On the space of slow growing weak Jacobi forms

Abstract

Keywords

ASJC Scopus subject areas

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