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Period functions for Maass wave forms and cohomology / R. Bruggeman, J. Lewis and D. Zagier.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 237, no 1118.Publication details: Providence : American Mathematical Society, 2015.Description: xii, 132 p. : illustrations ; 26 cmISBN:
  • 9781470414078 (pbk. : alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Eigenfunctions of the hyperbolic Laplace operator -- 2. Maass forms and analytic cohomology: cocompact groups -- 3. Cohomology of infinite cyclic subgroups of PSL₂(real numbers) -- 4. Maass forms and semi-analytic cohomology: groups with cusps -- 5. Maass forms and differentiable cohomology -- 6. Distribution cohomology and Petersson product -- Bibliography -- Index.
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
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 136673
Total holds: 0

Includes bibliographical references and index.

1. Eigenfunctions of the hyperbolic Laplace operator --
2. Maass forms and analytic cohomology: cocompact groups --
3. Cohomology of infinite cyclic subgroups of PSL₂(real numbers) --
4. Maass forms and semi-analytic cohomology: groups with cusps --
5. Maass forms and differentiable cohomology --
6. Distribution cohomology and Petersson product --
Bibliography --
Index.

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

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