Journal of Mathematics of Kyoto University

Siegel modular forms of half integral weight and a lifting conjecture

Shuichi Hayashida and Tomoyoshi Ibukiyama

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A conjecture on lifting to Siegel cusp forms of half-integral weight $k - 1/2$ of degree two from each pair of cusp forms of $SL_{2}(\mathbb{Z})$ of weight $2k - 2$ and $2k - 4$ is given with a conjectural relation of the $L$ functions and numerical evidences. We also describe the space of Siegel modular forms of half-integral weight, its “plus subspace” and Jacobi forms of degree two by explicitly given theta functions.

Article information

J. Math. Kyoto Univ., Volume 45, Number 3 (2005), 489-530.

First available in Project Euclid: 14 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F50: Jacobi forms


Hayashida, Shuichi; Ibukiyama, Tomoyoshi. Siegel modular forms of half integral weight and a lifting conjecture. J. Math. Kyoto Univ. 45 (2005), no. 3, 489--530. doi:10.1215/kjm/1250281971.

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