Skip to main content Accessibility help


  • Shunsuke Yamana (a1) (a2)

Following Jacquet, Lapid and Rogawski, we regularize trilinear periods. We use the regularized trilinear periods to compute Fourier–Jacobi periods of residues of Eisenstein series on metaplectic groups, which has an application to the Gan–Gross–Prasad conjecture.

Hide All
1. Bernstein, J. and Zelevinsky, A., Representations of the group GL(n, F), where F is a local non-Archimedean field, Uspekhi Mat. Nauk 31(3) (1976), 570 (in Russian); Engl. transl. in Russian Math. Surveys 31 (1976), 1–68.
2. Bernstein, J. and Zelevinsky, A., Induced representations of reductive p-adic groups, I, Ann. Sci. Éc. Norm. Supér. (4) 10 (1977), 441472.
3. Bump, D. and Ginzburg, D., Symmetric square L-functions on GL(r), Ann. of Math. (2) 136 (1992), 137205.
4. Casselman, W., Canonical extensions of Harish-Chandra modules to representations of G , Canad. J. Math. 41 (1989), 385438.
5. Cogdell, J., Piatetski-Shapiro, I. and Shahidi, F., Functoriality for the classical groups, Publ. Math. Inst. Hautes Études Sci. 99 (2004), 163233.
6. Gan, W. T., Gross, B. H. and Prasad, D., Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups, Astérisque 346 (2012), 1109.
7. Gelbart, S. and Piatetski-Shapiro, I., L-functions for G × GL (n), in Explicit Constructions of Automorphic L-functions, Lecture Notes in Mathematics, Volume 1254, pp. 53146 (Springer-Verlag, Berlin, 1987).
8. Ginzburg, D., Jiang, D. and Rallis, S., Nonvanishing of the central critical value of the third symmetric power L-functions, Forum Math. 13(1) (2001), 109132.
9. Ginzburg, D., Jiang, D. and Rallis, S., On the nonvanishing of the central value of the Rankin–Selberg L-functions, J. Amer. Math. Soc. 17(3) (2004), 679722.
10. Ginzburg, D., Jiang, D. and Rallis, S., On the nonvanishing of the central value of the Rankin–Selberg L-functions II, in Automorphic Representations, L-functions and Applications: Progress and Prospects, Ohio State Univ. Math. Res. Inst. Publ., Volume 11, pp. 157191 (de Gruyter, Berlin, 2005).
11. Ginzburg, D., Jiang, D. and Rallis, S., Models for certain residual representations of unitary groups, in Automorphic Forms and L-functions I: Global Aspects, Volume 488, pp. 125146. (2009). A volume in honor of S. Gelbart, Israel.
12. Ginzburg, D., Rallis, S. and Soudry, D., The Descent Map from Automorphic Representations of GL(n) to Classical Groups (World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011). x+339 pp.
13. Hanzer, M. and Muić, G., Parabolic induction and Jacquet functors for metaplectic groups, J. Algebra 323 (2010), 241260.
14. Ichino, A. and Yamana, S., Periods of automorphic forms: the case of (GL n+1 × GL n , GL n ), Compos. Math. 151 (2015), 665712.
15. Jacquet, H., Lapid, E. and Rogawski, J., Periods of automorphic forms, J. Amer. Math. Soc. 12 (1999), 173240.
16. Jacquet, H. and Shalika, J., On Euler products and the classification of automorphic representations I, Amer. J. Math. 103(3) (1981), 499558.
17. Jacquet, H. and Shalika, J., Exterior square L-functions, in Automorphic Forms, Shimura Varieties, and L-functions vol. II (ed. Clozel, L. and Milne, S.), pp. 143226. (1990).
18. Kaplan, E., The theta period of a cuspidal automorphic representation of GL(n), Int. Math. Res. Not. IMRN (8) (2015), 21682209.
19. Lapid, E. and Rogawski, J., Periods of Eisenstein series: the Galois case, Duke Math. J. 120(1) (2003), 153226.
20. Liu, Y. and Sun, B., Uniqueness of Fourier–Jacobi models: the Archimedean case, J. Funct. Anal. 265 (2013), 33253340.
21. Luo, W., Rudnick, Z. and Sarnak, P., On the generalized Ramanujan conjecture for GL(n), in Automorphic Forms, Automorphic Representations, and Arithmetic, Proceedings of Symposia in Applied Mathematics, Volume 66, pp. 301310 (American Mathematical Society, Providence, RI, 1999). Part 2.
22. Mœglin, C. and Waldspurger, J.-L., Spectral Decomposition and Eisenstein Series, Cambridge Tracts in Mathematics, Volume 113 (Cambridge University Press, Cambridge, 1995). xxviii+338 pp.
23. Ranga Rao, R., On some explicit formulas in the theory of Well representation, Pacific J. Math. 157 (1993), 335371.
24. Sun, B., Multiplicity one theorems for Fourier–Jacobi models, Amer. J. Math. 134(6) (2012), 16551678.
25. Szpruch, D., The Langlands–Shahidi method for the metaplectic group and applications, PhD thesis, Tel Aviv University (2009).
26. Wallach, N., Real Reductive Groups vol. II, Pure and Applied Mathematics, Volume 132 (Academic Press, Inc., Boston, MA, 1992). xiv+454 pp.
27. Yamana, S., Periods of residual automorphic forms, J. Funct. Anal. 268 (2015), 10781104.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Institute of Mathematics of Jussieu
  • ISSN: 1474-7480
  • EISSN: 1475-3030
  • URL: /core/journals/journal-of-the-institute-of-mathematics-of-jussieu
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


MSC classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed