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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Eichler cohomology theorem for automorphic forms of small weights


Authors: Marvin Knopp and Henok Mawi
Journal: Proc. Amer. Math. Soc. 138 (2010), 395-404
MSC (2000): Primary 11F12, 11F75
Published electronically: October 2, 2009
MathSciNet review: 2557156
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Abstract: Let $ \Gamma$ be an $ H$-group. In 1974 Marvin Knopp conjectured that the Eichler cohomology group, with base space taken to be the set of all functions holomorphic in the upper half-plane, of polynomial growth at the real line (including $ \infty$), and with a weight $ k,$multiplier system $ v$ linear fractional action of $ \Gamma$, is isomorphic to the space of cusp forms on $ \Gamma$ of weight $ 2-k$ and multiplier system $ \overline{v}$, in the range $ 0<k<2$. In this article the authors prove the conjecture by making essential use of Hans Petersson's ``principal parts condition'' for automorphic forms (1955).


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Additional Information

Marvin Knopp
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Henok Mawi
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10070-9
Keywords: Automorphic forms, automorphic integrals, Eichler cohomology
Received by editor(s): November 18, 2008
Published electronically: October 2, 2009
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2009 American Mathematical Society