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Transportable Modular Symbols and the Intersection Pairing

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Book cover Algorithmic Number Theory (ANTS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2369))

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Abstract

Transportable modular symbols were originally introduced in order to compute periods of modular forms [18]. Here we use them to give an algorithm to compute the intersection pairing for modular symbols of weight k ≥ 2. This generalizes the algorithm given by Merel [13] for computing the intersection pairing for modular symbols of weight 2. We also define a certain subspace of the space of transportable modular symbols, and give numerical evidence to support a conjecture that this space should replace the usual space of cuspidal modular symbols.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Hannover, Postfach 6009, D 30060, Hannover, Germany

    Helena A. Verrill

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  1. Helena A. Verrill
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, F07, University of Sydney, Sydney, NSW, 2006, Australia

    Claus Fieker  & David R. Kohel  & 

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Verrill, H.A. (2002). Transportable Modular Symbols and the Intersection Pairing. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_18

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  • DOI: https://doi.org/10.1007/3-540-45455-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43863-2

  • Online ISBN: 978-3-540-45455-7

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