Proofs of Ibukiyama’s conjectures on Siegel modular forms of half-integral weight and of degree 2
Proofs of Ibukiyama’s conjectures on Siegel modular forms of half-integral weight and of degree 2
复制标题
DOI：
10.1007/s00208-021-02232-4
复制
发表时间：
2020-10
影响因子：
1.4
通讯作者：
H. Ishimoto
中科院分区：
文献类型：
--
作者：
H. Ishimoto
我们利用分裂奇特殊正交群上的Arthur重数公式和Metaplectic群上的Gan-Ichino重数公式证明了Ibukiyama关于半积分权2次Siegel模形式的猜想。在证明中，雅可比群的表示论也发挥了重要作用。
We prove Ibukiyama’s conjectures on Siegel modular forms of half-integral weight and of degree 2 by using Arthur’s multiplicity formula on the split odd special orthogonal groupand Gan–Ichino’s multiplicity formula on the metaplectic group. In the proof, the representation theory of the Jacobi groups also plays an important role.