Abstract
In this paper, we compute the local integrals, with normalized unramified data, over a p-adic field F, arising from general Rankin–Selberg integrals for SO m × GLr+k+1, where the orthogonal group is split over F, $$k \leqslant \left[ {\frac{{m - 1}}{2}} \right]$$ , and the irreducible representation of SO m (F) has a Bessel model with respect to an irreducible representation of the split orthogonal group SOm−2k−1(F). Our proof is by “analytic continuation from the unramified computation in the generic case”. We let the unramified parameters of the representations involved vary, and express the local integrals in terms of the Whittaker models of the representations, which exist at points in general position. Then we apply analytic continuation and the known unramified computation in the generic case. We discuss some applications to poles of partial L-functions and functorial lifting.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.