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Period Functions for Maass Wave Forms and Cohomology - R. Bruggeman, J. Lewis, D. Zagier

Period Functions for Maass Wave Forms and Cohomology

Buch | Softcover
132 Seiten
2015
American Mathematical Society (Verlag)
978-1-4704-1407-8 (ISBN)
CHF 137,40 inkl. MwSt
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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.
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.

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.

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 produc
Bibliography
Index
List of notations

Reihe/Serie Memoirs of the American Mathematical Society
Verlagsort Providence
Sprache englisch
Maße 178 x 254 mm
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
ISBN-10 1-4704-1407-4 / 1470414074
ISBN-13 978-1-4704-1407-8 / 9781470414078
Zustand Neuware
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