Modular forms associated to closed geodesics and arithmetic applications

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

For any Fuchsian group of the first kind and any even weight greater than 2, we prove that the relative Poincaré series associated to closed geodesics generate the space of cusp forms of the given weight. Those series have very interesting geometrical and arithmetic properties. For arithmetic subgroups of SL2R (with or without cusps), our construction allows us to define two natural rational structures on the space of cusp forms.

Original languageEnglish (US)
Pages (from-to)177-179
Number of pages3
JournalBulletin of the American Mathematical Society
Volume11
Issue number1
DOIs
StatePublished - Jul 1984

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Closed Geodesics
Cusp Form
Modular Forms
Fuchsian Group
Series
Cusp
Subgroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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title = "Modular forms associated to closed geodesics and arithmetic applications",
abstract = "For any Fuchsian group of the first kind and any even weight greater than 2, we prove that the relative Poincar{\'e} series associated to closed geodesics generate the space of cusp forms of the given weight. Those series have very interesting geometrical and arithmetic properties. For arithmetic subgroups of SL2R (with or without cusps), our construction allows us to define two natural rational structures on the space of cusp forms.",
author = "Svetlana Katok",
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Modular forms associated to closed geodesics and arithmetic applications. / Katok, Svetlana.

In: Bulletin of the American Mathematical Society, Vol. 11, No. 1, 07.1984, p. 177-179.

Research output: Contribution to journalArticle

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