Abstract
Let k be a local field. Let Iv and Iv′ be smooth principal series representations of GLn(k) and GLn-−1(k), respectively. The Rankin-Selberg integrals yield a continuous bilinear map Iv×Iv′→C with a certain invariance property. We study integrals over a certain open orbit that also yield a continuous bilinear map Iv×Iv′→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).
Original language | English |
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Pages (from-to) | 2203-2218 |
Number of pages | 16 |
Journal | Science China Mathematics |
Volume | 66 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2023 |
Keywords
- 22E50
- 43A80
- L-functions
- Rankin-Selberg convolutions
- principal series representations