Work

Computing Jacobi forms

Year: 2016

Type: article

Abstract: We describe an implementation for computing holomorphic and skew-holomorphic Jacobi forms of integral weight and scalar index on the full modular group. This implementation is based on formulas derived by one of the authors which express Jacobi forms in terms of modular symbols of elliptic modular forms. Since this method allows a Jacobi eigenform to be generated directly from a given modular eigensymbol without reference to the whole ambient space of Jacobi forms, it makes it possible to compute Jacobi Hecke eigenforms of large index. We illustrate our method with several examples.

Source: LMS Journal of Computation and Mathematics

DOI: 10.1112/s1461157016000346

Authors: Nathan C. Ryan, Nicolás Sirolli, Nils-Peter Skoruppa, Gonzalo Tornaría

Institutions: Bucknell University, Universidad de la República de Uruguay, Universidad de Buenos Aires, University of Siegen

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Agencia Nacional de Investigación e Innovación, University of Cambridge, Centro Nacional de Investigaciones Cardiovasculares

Award: US collaboration with Argentina, Chile, and Uruguay: Modular Forms in the Southern Cone