Period Functions for Maass Wave Forms and Cohomology (Memoirs of the American Mathematical Society) - Image 1

£79.95

American Mathematical Society Period Functions for Maass Wave Forms and Cohomology (Memoirs of the American Mathematical Society)

Name: Period Functions for Maass Wave Forms and Cohomology (Memoirs of the American Mathematical Society)
Brand: American Mathematical Society
Price: 79.95 GBP
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Mathematical Theory

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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 series representation. This enables them to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all $\Gamma$-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms the authors also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. They use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology. About the Author R. Bruggeman, Mathematisch Instituut, Universiteit Utrecht, The Netherlands. J. Lewis, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. D. Zagier, MPI for Mathematics, Bonn, Germany, and College de France, Paris, France.

Product Specifications

Brand: American Mathematical Society
Format: paperback
ASIN: 1470414074
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Theory
Domain: Amazon UK
Release Date: 30 August 2015
Listed Since: 18 June 2015

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American Mathematical Society Period Functions for Maass Wave Forms and Cohomology (Memoirs of the American Mathematical Society)

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