Abstract
It was proved by Ibukiyama and Skoruppa that the spaces J 1,m (l) of Jacobi forms of weight 1, index m and level l vanish if gcd (l,m)=1. We will show that the result holds without the gcd hypothesis.
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Eichler, M., Zagier, D.: The Theory of Jacobi Forms. Progress in Mathematics, vol. 55. Birkhäuser, Boston (1985)
Ibukiyama, T., Skoruppa, N.-P.: A vanishing theorem for Siegel modular forms of weight one. Abh. Math. Semin. Univ. Hamb. 77, 229–235 (2007)
Skoruppa, N.-P.: Über den Zusammenhang zwischen Jacobiformen und Modulformen halbganzen Gewichts. Inaugural-Dissertation, Bonner Mathematische Schriften, vol. 159, Bonn (1984)
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Communicated by U. Kühn.
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Schmidt, R. A remark on a paper of Ibukiyama and Skoruppa. Abh. Math. Semin. Univ. Hambg. 79, 189–191 (2009). https://doi.org/10.1007/s12188-009-0026-z
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DOI: https://doi.org/10.1007/s12188-009-0026-z