## Journal of Mathematics of Kyoto University

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

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

Shuichi Hayashida and Tomoyoshi Ibukiyama

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1215/kjm/1250281971

**Mathematical Reviews number (MathSciNet)**

MR2206360

**Zentralblatt MATH identifier**

1122.11028

**Subjects**

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

#### 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