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Relative Kloosterman Integrals For Gl(3): III

Published online by Cambridge University Press:  20 November 2018

Zhengyu Mao
Zhengyu Mao*
Affiliation:
Mathematics Department Columbia University New York City, New York, 10027 USA.
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Abstract

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Let E be a quadratic extension of a number field F with Galois conjugation σ, G’ the quasi-split unitary group in three variables, G the group GL(3, E). We let S be the space of the matrices s in G such that σ(s)s = e. One conjectures a comparison identity between the relative Kuznietsov trace formula for the symmetric space S and the ordinary Kuznietsov trace formula for the group G’ (See [10]). We prove the corresponding “fundamental lemmas”.

Keywords

11F72Kahler manifoldsformalityequivariant minimal models
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 6 , 01 December 1993 , pp. 1211 - 1230
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Casselman, W. and Shalika, J., The unramified principal series ofp-adic groups II: the Whittaker function, Comp. Math. 41(1980), 207–231.Google Scholar
2. Flicker, Y., On distinguished representations, J. reine, angew. Math. 418(1991), 139–172.Google Scholar
3. Flicker, Y., Distinguished representations and a Fourier trace formula, Bull. Soc. Math. France, to appear.Google Scholar
4. Friedberg, S., Poincaré series for GL(rc): Fourier expansions, Kloosterman sums, and algebreo-geometricestimate, Math. Zeit. 196(1987), 165–188.Google Scholar
5. Goldfeld, D., Kloosterman zeta functions for GL(rc,Z), Proc. Intern. Cong. Math., Berkeley, 1(1986), 417–424.Google Scholar
6. Harder, G., Langlands, R.P. and Rapoport, M., Algebraische Zyklen auf Hilbert-Blumenthal-Fldchen, Journal Fur Math. 366(1986), 53–120.Google Scholar
7. Jacquet, H., Relative Kloosterman integrals for GL(3).77, Canadian J. Math., 44(1992. 1220–1240.Google Scholar
8. Jacquet, H., On the nonvanishing of some L-functions, Proc. Indian. Acad. Sci. (Math) 97(1987), 117–155.Google Scholar
9. Jacquet, H. and Ye, Y., Relative Kloosterman Integrals for GL(3), Bull. Soc. Math. France. 119(1991), 101–133.Google Scholar
10. Jacquet, H. and Ye, Y. , Une remarque sur le changement de base quadratique, C.R. Acad. Sci. Paris 311(1990), 671–676.Google Scholar
11. Rogawski, J., Automorphic Representations of Unitary Groups in Three Variables, Annals of Mathematics Studies 123, Princeton University Press, 1990.Google Scholar
12. Springer, T., Some results on algebraic groups with involution. In: Algebraic Groups and Related Topics, Advanced Studies in Mathematics 6, Tokyo, (1984), 323–343.Google Scholar
13. Stevens, G., Poincaré series on GL(r) and Kloosterman sums, Math. Ann. 277(1987), 25–51.Google Scholar
14. Ye, Y., Kloosterman integrals and base change for GL(2), J. reine, angew. Math. 400(1989), 57–121.Google Scholar