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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing genus $1$ Jacobi forms
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by Martin Raum PDF
Math. Comp. 85 (2016), 931-960 Request permission

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
  • Email: martin@raum-brothers.eu
  • 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.
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 931-960
  • MSC (2010): Primary 11F30, 11G18; Secondary 11F50, 11F27
  • DOI: https://doi.org/10.1090/mcom/2992
  • MathSciNet review: 3434889