On the space of slow growing weak Jacobi forms

Christoph A. Keller, Jason M. Quinones

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)730-750
Number of pages21
JournalJournal of Number Theory
Volume240
DOIs
StatePublished - Nov 2022

Keywords

  • Automorphic forms
  • Holography
  • Jacobi forms
  • Modular forms
  • Theta series

ASJC Scopus subject areas

  • Algebra and Number Theory

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