Rankin-Selberg convolutions for GL(n)×GL(n)and GL(n)×GL(n-1)for principal series representations  

作　　者：Jian-Shu Li Dongwen Liu Feng Su Binyong Sun 

机构地区：[1]Institute for Advanced Study in Mathematics,Zhejiang University,Hangzhou 310058,China [2]School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China [3]Department of Pure Mathematics,Xi’an Jiaotong-Liverpool University,Suzhou 215123,China

出　　处：《Science China Mathematics》2023年第10期2203-2218,共16页中国科学：数学（英文版）

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).

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).

关 键 词：principal series representation Rankin-Selberg convolution L-FUNCTION 

分 类 号：O173[理学—数学]