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Computing Borcherds products

Part of: Computational number theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 August 2013

Dominic Gehre ,
Judith Kreuzer  and
Martin Raum
Dominic Gehre
Affiliation:
Lehrstuhl A für Mathematik,RWTH Aachen University,Templergraben 55, D-52056 Aachen,Germany email dominic.gehre@matha.rwth-aachen.dejudith.kreuzer@matha.rwth-aachen.de
Judith Kreuzer
Affiliation:
Lehrstuhl A für Mathematik,RWTH Aachen University,Templergraben 55, D-52056 Aachen,Germany email dominic.gehre@matha.rwth-aachen.dejudith.kreuzer@matha.rwth-aachen.de
Martin Raum
Affiliation:
ETH Mathematics Department,Rämistraße 101, CH-8092, Zürich,Switzerland email martin.raum@math.ethz.ch

Abstract

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We present an algorithm for computing Borcherds products, which has polynomial runtime. It deals efficiently with the bounds on Fourier expansion indices originating in Weyl chambers. Naive multiplication has exponential runtime due to inefficient handling of these bounds. An implementation of the new algorithm shows that it is also much faster in practice.

MSC classification

Secondary: 11F55: Other groups and their modular and automorphic forms (several variables) 11F30: Fourier coefficients of automorphic forms 11Y16: Algorithms; complexity 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013 , pp. 200 - 215
Copyright
© The Author(s) 2013 

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