Modular forms associated to closed geodesics and arithmetic applications

Svetlana Katok

doi:10.1090/S0273-0979-1984-15257-1

Modular forms associated to closed geodesics and arithmetic applications

Svetlana Katok

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7 Scopus citations

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 language	English (US)
Pages (from-to)	177-179
Number of pages	3
Journal	Bulletin of the American Mathematical Society
Volume	11
Issue number	1
DOIs	https://doi.org/10.1090/S0273-0979-1984-15257-1
State	Published - Jul 1984

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0273-0979-1984-15257-1

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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AB - 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.

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ER -

Modular forms associated to closed geodesics and arithmetic applications

Abstract

All Science Journal Classification (ASJC) codes

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