摘要
Let k be a local field.Let I_(v) and I_(v′)be smooth principal series representations of GLn(k)and GL_(n-1)(k),respectively.The Rankin-Selberg integrals yield a continuous bilinear map I_(v)×I_(v′)→C with a certain invariance property.We study integrals over a certain open orbit that also yield a continuous bilinear map I_(v)×I_(v′)→C with the same invariance property and show that these integrals equal the Rankin-Selberg integrals up to an explicit constant.Similar results are also obtained for Rankin-Selberg integrals for GLn(k)×GLn(k).
基金
supported by the Natural Science Foundation of Zhejiang Province(Grant No.LZ22A010006)
National Natural Science Foundation of China(Grant No.12171421)
Feng Su was supported by National Natural Science Foundation of China(Grant No.11901466)
the Qinglan Project of Jiangsu Province
supported by the National Key Research and Development Program of China(Grant No.2020YFA0712600).
