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.
Author: | Oliver Stein |
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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 |