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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

E. Bulla1 / D. Constales2 / R. S. Kraußhar3 / John Ryan4

1Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. e-mail:

2Department of Mathematical Analysis, Ghent University, Building S-22, Galglaan 2, 9000 Ghent, Belgium. e-mail:

3Lehrstuhl für Komplexe Systeme, Institut für Mathematik, Universität Paderborn, Warburgerstr. 100, 33098 Paderborn, Germany. e-mail:

4Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 643, Pages 1–19, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2010.042, June 2010

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Fundamental solutions of Dirac type operators are introduced for a class of conformally flat spin manifolds. This class consists of manifolds obtained by factoring out the upper half-space of by congruence subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented together with associated Eisenstein and Poincaré type series.

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