On the smooth transfer conjecture of Jacquet–Rallis for n=3
- 234 Downloads
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.
KeywordsRelative trace formula Shalika germs Smooth transfer
Mathematics Subject Classification22E35 11F85
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.
- 4.Jacquet, H., Rallis, S.: On the Gross–Prasad conjecture for unitary groups. In: On Certain L-functions. Clay Math. Proc., vol. 13, pp. 205–264. Am. Math. Soc., Providence (2011) Google Scholar
- 9.Zhang, W.: Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups. Preprint (2011) Google Scholar