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Linear relations between Fourier coefficients of special Siegel modular forms

Published online by Cambridge University Press:  22 January 2016

Winfried Kohnen*
Affiliation:
Universität Heidelberg, Mathematisches Institut, INF 288, D-69120 Heidelberg, Germany, winfried@mathi.uni-heidelberg.de
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Abstract

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In this paper we give certain linear relations between the Fourier coefficients of Siegel modular forms that are obtained from Ikeda lifts.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

[1] Böcherer, S., Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen, manuscripta math., 45 (1984), 273288.CrossRefGoogle Scholar
[2] Böcherer, S. and Kohnen, W., On the functional equation of singular series, Abh. Math. Sem. Univ. Hamburg, 70 (2000), 281286.CrossRefGoogle Scholar
[3] Cassels, J.W.S., Rational quadratic forms, Academic Press, London New York San Francisco, 1978.Google Scholar
[4] Eichler, M. and Zagier, D., The theory of Jacobi forms: Progress in Math., vol. 55, Birkhäuser, Boston, 1985.CrossRefGoogle Scholar
[5] Ikeda, T., On the lifting of elliptic modular forms to Siegel cusp forms of degree 2n, Ann. Math., 154, no. 3 (2001), 641681.CrossRefGoogle Scholar
[6] Katsurada, H., An explicit form for Siegel series, Amer. J. Math., 121 (1999), 415452.CrossRefGoogle Scholar
[7] Kitaoka, Y., Dirichlet series in the theory of Siegel modular forms, Nagoya Math. J., 95 (1984), 7384.CrossRefGoogle Scholar
[8] Kitaoka, Y., Arithmetic of quadratic forms: Cambridge Texts in Math., vol 106, Cambridge Univ. Press, Cambridge, 1999.Google Scholar
[9] Kohnen, W., Modular forms of half-integral weight on Γ0(4), Math. Ann., 248 (1980), 249266.CrossRefGoogle Scholar
[10] Kohnen, W., Lifting modular forms of half-integral weight to Siegel modular forms of even genus, Math. Ann., 322 (2002), 787809.CrossRefGoogle Scholar
[11] O’Meara, O.T., Introduction to quadratic forms: Grundl. d. Math. Wiss., vol. 117, Springer, Berlin Heidelberg New York, 1963.Google Scholar
[12] Shimura, G., On modular forms of half-integral weight, Ann. of Math., 97 (1973), 440481.Google Scholar