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 ce...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).展开更多
基金supported by the Natural Science Foundation of Zhejiang Province(Grant No.LZ22A010006)National Natural Science Foundation of China(Grant No.12171421)+2 种基金Feng Su was supported by National Natural Science Foundation of China(Grant No.11901466)the Qinglan Project of Jiangsu Provincesupported by the National Key Research and Development Program of China(Grant No.2020YFA0712600).
文摘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).
