| Description |
1 online resource (xii, 132 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 237, number 1118 |
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Memoirs of the American Mathematical Society ; no. 1118.
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| Contents |
Introduction -- Eigenfunctions of the hyperbolic Laplace operator -- Maass forms and analytic cohomology: cocompact groups -- Cohomology of infinite cyclic subgroups of PSL₂(R) -- Maass forms and semi-analytic cohomology: groups with cusps -- Maass forms and differentiable cohomology -- Distribution cohomology and Petersson product -- Bibliography -- Index -- List of notations |
| Summary |
The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups \Gamma\subset\mathrm{PSL}_2({\mathbb{R}}). In the case that \Gamma is the modular group \mathrm{PSL}_2({\mathbb{Z}}) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal serie |
| Bibliography |
Includes bibliographical references (pages 127-128) and index |
| Notes |
"Volume 237, number 1118 (second of 6 numbers), September 2015." |
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Online resource; title from PDF title page (viewed October 6, 2015) |
| Subject |
Forms, Modular.
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Forms (Mathematics)
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Cohomology operations.
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Algebraic topology.
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Algebraic topology
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Cohomology operations
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Forms (Mathematics)
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Forms, Modular
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| Form |
Electronic book
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| Author |
Lewis, J. (John B), 1944- author.
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Zagier, Don, 1951- author.
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American Mathematical Society, publisher
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| ISBN |
9781470425036 |
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1470425033 |
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