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

 

Multiplicities of representations in spaces of modular forms


Author: Bin Yong Hsie
Journal: Proc. Amer. Math. Soc. 134 (2006), 1-3
MSC (2000): Primary 11F11
Published electronically: August 19, 2005
MathSciNet review: 2170535
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper shows that for a given irreducible representation $\rho $ of $\Gamma /\Gamma _{1}$, the two functions dim( $M_{k}(\Gamma _{1},\rho )$) and dim( $S_{k}(\Gamma _{1},\rho )$) of $k$are almost linear functions.


References [Enhancements On Off] (What's this?)

  • 1. Otto Forster, Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, New York-Berlin, 1981. Translated from the German by Bruce Gilligan. MR 648106 (83d:30046)
  • 2. Neal Koblitz, Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics, vol. 97, Springer-Verlag, New York, 1984. MR 766911 (86c:11040)
  • 3. Jean-Pierre Serre, Linear representations of finite groups, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott; Graduate Texts in Mathematics, Vol. 42. MR 0450380 (56 #8675)
  • 4. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, Princeton, New Jersey, 1971.

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Additional Information

Bin Yong Hsie
Affiliation: LMAM, Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China
Email: byhsie@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08289-4
PII: S 0002-9939(05)08289-4
Keywords: Modular form, cusp form
Received by editor(s): June 4, 2004
Published electronically: August 19, 2005
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.