Generating weights for the Weil representation attached to an even order cyclic quadratic module

Luca Candelori, Cameron Franc, Gene Kopp

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
204 Downloads (Pure)

Abstract

We develop geometric methods to study the generating weights of free modules of vector-valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group. We then compute the generating weights for modular forms taking values in the Weil representation attached to cyclic quadratic modules of order $2p^r$, where $p \geq 5$ is a prime. We also show that the generating weights approach a simple limiting distribution as $p$ grows, or as $r$ grows and $p$ remains fixed.
Original languageEnglish
Pages (from-to)474-497
Number of pages24
JournalJournal of Number Theory
Volume180
Early online date23 Jun 2017
DOIs
Publication statusPublished - 1 Nov 2017

Keywords

  • vector-valued modular form
  • half-integral weight
  • Weil representation
  • quadratic module
  • generating weights
  • metaplectic group
  • metaplectic orbifold
  • critical weights
  • Serre duality
  • Dirichlet class number formula
  • imaginary quadratic field
  • positive-definite lattice
  • quadratic form
  • theta function

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