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Computing Borcherds products

Published online by Cambridge University Press:  01 August 2013

Dominic Gehre
Affiliation:
Lehrstuhl A für Mathematik,RWTH Aachen University,Templergraben 55, D-52056 Aachen,Germany email [email protected]@matha.rwth-aachen.de
Judith Kreuzer
Affiliation:
Lehrstuhl A für Mathematik,RWTH Aachen University,Templergraben 55, D-52056 Aachen,Germany email [email protected]@matha.rwth-aachen.de
Martin Raum
Affiliation:
ETH Mathematics Department,Rämistraße 101, CH-8092, Zürich,Switzerland email [email protected]

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.

Type
Research Article
Copyright
© The Author(s) 2013 

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