Functiones et Approximatio Commentarii Mathematici

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

Oliver Stein

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Abstract

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.

Article information

Source
Funct. Approx. Comment. Math., Volume 52, Number 2 (2015), 229-252.

Dates
First available in Project Euclid: 18 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.facm/1434650879

Digital Object Identifier
doi:10.7169/facm/2015.52.2.4

Mathematical Reviews number (MathSciNet)
MR3358318

Zentralblatt MATH identifier
06862260

Subjects
Primary: 11F25: Hecke-Petersson operators, differential operators (one variable) 11F27: Theta series; Weil representation; theta correspondences
Secondary: 11L05: Gauss and Kloosterman sums; generalizations 11E08: Quadratic forms over local rings and fields

Keywords
Fourier expansion Hecke operators vector-valued modular forms Weil representation Gauss sums

Citation

Stein, Oliver. The Fourier expansion of Hecke operators for vector-valued modular forms. Funct. Approx. Comment. Math. 52 (2015), no. 2, 229--252. doi:10.7169/facm/2015.52.2.4. https://projecteuclid.org/euclid.facm/1434650879


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