Author: Roelof W. Bruggeman
Publisher:
Published: 2015
Total Pages: 132
ISBN-13: 9781470425036
DOWNLOAD EBOOKWe construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ ⊂ PSL2(R). In the case that Γ is the modular group PSL2(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. We introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables us to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms we also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. We use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.
Book Synopsis Period Functions for Maass Wave Forms and Cohomology by : Roelof W. Bruggeman
Download or read book Period Functions for Maass Wave Forms and Cohomology written by Roelof W. Bruggeman and published by . This book was released on 2015 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups Γ ⊂ PSL2(R). In the case that Γ is the modular group PSL2(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. We introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal series representation. This enables us to describe cohomology groups isomorphic to spaces of Maass cusp forms, spaces spanned by residues of Eisenstein series, and spaces of all Γ-invariant eigenfunctions of the Laplace operator. For spaces of Maass cusp forms we also describe isomorphisms to parabolic cohomology groups with smooth coefficients and standard cohomology groups with distribution coefficients. We use the latter correspondence to relate the Petersson scalar product to the cup product in cohomology.