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Mathematics of Computation

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Computing genus $ 1$ Jacobi forms

Author: Martin Raum
Journal: Math. Comp. 85 (2016), 931-960
MSC (2010): Primary 11F30, 11G18; Secondary 11F50, 11F27
Published electronically: July 7, 2015
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Abstract: We develop an algorithm to compute Fourier expansions of vector valued modular forms for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three families of Hecke operators for Jacobi forms, and analyze the induced action on vector valued modular forms. The newspaces attached to one of these families are used to give a more memory efficient version of our algorithm.

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Additional Information

Martin Raum
Affiliation: ETH, Department of Mathematics, Rämistraße 101, CH-8092, Zürich, Switzerland
Address at time of publication: Chalmers tekniska högskola, Institutionen för Matematiska vetenskaper Martin Westerholt-Raum, SE-412 96 Göteborg, Sweden

Keywords: Fourier expansions of vector valued modular forms, special divisors, Hecke operators
Received by editor(s): October 4, 2013
Received by editor(s) in revised form: June 5, 2014, August 25, 2014, and September 1, 2014
Published electronically: July 7, 2015
Additional Notes: The author was supported by the ETH Zurich Postdoctoral Fellowship Program and by the Marie Curie Actions for People COFUND Program.
Article copyright: © Copyright 2015 American Mathematical Society