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The Ramanujan Journal

, Volume 29, Issue 1–3, pp 225–256 | Cite as

On the smooth transfer conjecture of Jacquet–Rallis for n=3

  • Wei ZhangEmail author
Article

Abstract

We obtain a relative Shalika germ expansion of orbital integrals appeared in the relative trace formulae Jacquet–Rallis when n=3. This is the first example where there are infinitely many nilpotent orbits. As an application we can prove the smooth transfer conjecture of Jacquet–Rallis for n=3.

Keywords

Relative trace formula Shalika germs Smooth transfer 

Mathematics Subject Classification

22E35 11F85 

Notes

Acknowledgements

The author thanks the anonymous referee for pointing out the application to the density principle and for several comments on improving the exposition. He also thanks the Institute for Advanced Studies at the Hong Kong University of Science and Technology for their hospitality where the result was represented in a workshop in December 2011.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA

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