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The Fourier expansion of Hecke operators for vector-valued modular forms

  • We compute the Fourier expansion of Hecke operators on vector-valued modular forms for the Weil representation associated to a lattice L. The Hecke operators considered in this paper include operators T(p^2l) where p is a prime dividing the level of the lattice L. Additionally, an explicit formula for a general type of Gauss sum associated to a lattice L drops out as a by-product.

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Metadaten
Author:Oliver Stein
DOI:https://doi.org/10.7169/facm/2015.52.2.4
ISSN:2080-9433
Parent Title (English):Functiones et Approximatio Commentarii Mathematici
Publisher:Adam Mickiewicz University, Faculty of Mathematics and Computer Science
Place of publication:Poznań
Document Type:Article
Language:English
Year of first Publication:2015
Release Date:2023/01/18
Volume:52
Issue:2
First Page:229
Last Page:252
Note:
Correction and addendum to: The Fourier expansion of Hecke operators for vector-valued modular forms unter: https://doi.org/10.7169/facm/1969
We correct a mistake in [St] leading to erroneous formulas in Theorems 5.2 and 5.4. As an immediate corollary of a formula in [BCJ] we give a formula which relates the Hecke operators T(p2)∘T(p2l−2), T(p2l) and T(p2l−4) and comment on it.
Institutes:Fakultät Informatik und Mathematik
Begutachtungsstatus:peer-reviewed
OpenAccess Publikationsweg:Gold Open Access- Erstveröffentlichung in einem/als Open-Access-Medium
Licence (German):Keine Lizenz - Es gilt das deutsche Urheberrecht: § 53 UrhG