## Journal of Mathematics of Kyoto University

### Siegel modular forms of half integral weight and a lifting conjecture

#### Abstract

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

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

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250281971

Digital Object Identifier
doi:10.1215/kjm/1250281971

Mathematical Reviews number (MathSciNet)
MR2206360

Zentralblatt MATH identifier
1122.11028

#### Citation

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. https://projecteuclid.org/euclid.kjm/1250281971