复数上Waldspurger对应中的Bessel恒等式
Bessel Identities in the Waldspurger Correspondence over the Complex Numbers
摘要：
证明了$\mathrm{PGL}_2(\mathbb{C})$的不可约酉表示与$\mathrm{SL}_2 (\mathbb{C})$的不可约酉表示上的相对Bessel函数之间的某些恒等式.这些恒等式反映了在$\mathbb{C}$上的Waldspurger对应。我们还证明了出现在相对迹公式中的Bessel分布和相对Bessel分布的几个正则性定理。本文建立了$\mathbb{C}$上Jacquet相对迹公式的局部谱理论.
英文摘要：
We prove certain identities between relative Bessel functions attached to irreducible unitary representations of $\mathrm{PGL}_2(\mathbb{C})$ and Bessel functions attached to irreducible unitary representations of $\mathrm{SL}_2 (\mathbb{C})$. These identities reflect the Waldspurger correspondence over $\mathbb{C}$. We also prove several regularity theorems for Bessel and relative Bessel distributions which appear in the relative trace formula. This paper constitutes the local spectral theory of Jacquet's relative trace formula over $\mathbb{C}$.
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