Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 1

Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms

Pages: 21 – 47

DOI: http://dx.doi.org/10.4310/PAMQ.2015.v11.n1.a2

Authors

Fabien Cléry (Department Mathematik, Universität Siegen, Germany)

Gerard van der Geer (Korteweg-de Vries Instituut, Universiteit van Amsterdam, The Netherlands)

Abstract

This paper gives a simple method for constructing vector-valued Siegel modular forms from scalar-valued ones. The method is efficient in producing the siblings of Delta, the smallest weight cusp forms that appear in low degrees. It also shows the strong relations between these modular forms of different degrees. We illustrate this by a number of examples.

Keywords

Siegel modular form, vector-valued modular form

2010 Mathematics Subject Classification

14J15

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