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Mathematische Zeitschrift

, 264:1 | Cite as

On newforms for Kohnen plus spaces

  • Masaru Ueda
  • Shunsuke Yamana
Article

Abstract

In this article, we investigate the plus space of level N, where 4−1 N is a square-free (not necessarily odd) integer. This is a generalization of Kohnen’s work. We define a Hecke isomorphism \({\wp_k}\) of M k+1/2(4M) onto \({M_{k+1/2}^+(8M)}\) for any odd positive integer M. The methods of the proof of the newform theory are this isomorphism, Waldspurger’s theorem, and the dimension identity.

Keywords

Forms of half-integral weight Newforms Shimura correspondence Kohnen plus space 

Mathematics Subject Classification (2000)

11F37 

References

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    Serre, J.P., Stark, H.M.: Modular forms of weight 1/2. Springer Lec. notes in Math., vol. 627, pp. 27–67 (1977)Google Scholar
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    Ueda M.: The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators. J. Math. Kyoto Univ. 28, 505–555 (1988)zbMATHMathSciNetGoogle Scholar
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    Ueda M.: On twisting operators and newforms of half-integral weight. Nagoya. Math. J. 131, 135–205 (1993)zbMATHMathSciNetGoogle Scholar
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    Waldspurger J.L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl. 60, 375–484 (1981)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceNara Women’s UniversityNaraJapan
  2. 2.Graduate School of MathematicsKyoto UniversityKyotoJapan

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