Geodesic
Periods of automorphic forms
Jacquet, Hervé1 ; Lapid, Erez2 ; Rogawski, Jonathan3, 4
1 Department of Mathematics, Columbia University, New York, New York 10027
2 Department of Mathematics, Weizmann Institute, Rehovot, Israel
3 Department of Mathematics, Hebrew University, Jerusalem, Israel
4 Department of Mathematics, University of California, Los Angeles, California 90095
Journal of the American Mathematical Society, Tome 12 (1999) no. 1, pp. 173-240

Voir la notice de l'article provenant de la source American Mathematical Society

Let $E/F$ be a quadratic extension of number fields and $G= \operatorname {Res}_{E/F}H$, where $H$ is a reductive group over $F$. We define the integral (in general, non-convergent) of an automorphic form on $G$ over $H(F)\backslash H(\mathbb A)^1$ via regularization. This regularized integral is used to derive a formula for the integral over $H(F)\backslash H(\mathbb A)^1$ of a truncated Eisenstein series on $G$. More explicit results are obtained in the case $H=GL(n)$. These results will find applications in the expansion of the spectral side of the relative trace formula.
DOI : 10.1090/S0894-0347-99-00279-9

Jacquet, Hervé 1 ; Lapid, Erez 2 ; Rogawski, Jonathan 3, 4

1 Department of Mathematics, Columbia University, New York, New York 10027
2 Department of Mathematics, Weizmann Institute, Rehovot, Israel
3 Department of Mathematics, Hebrew University, Jerusalem, Israel
4 Department of Mathematics, University of California, Los Angeles, California 90095 
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Jacquet, Hervé; Lapid, Erez; Rogawski, Jonathan. Periods of automorphic forms. Journal of the American Mathematical Society, Tome 12 (1999) no. 1, pp. 173-240. doi: 10.1090/S0894-0347-99-00279-9

[1] Arthur, James G. A trace formula for reductive groups. I. Terms associated to classes in 𝐺(𝑄) Duke Math. J. 1978 911 952

[2] Arthur, James A trace formula for reductive groups. II. Applications of a truncation operator Compositio Math. 1980 87 121

[3] Arthur, James The trace formula in invariant form Ann. of Math. (2) 1981 1 74

[4] Arthur, James On the inner product of truncated Eisenstein series Duke Math. J. 1982 35 70

[5] Asai, Tetsuya On certain Dirichlet series associated with Hilbert modular forms and Rankin’s method Math. Ann. 1977 81 94

[6] Bernstein, I. N., Zelevinsky, A. V. Induced representations of reductive 𝔭-adic groups. I Ann. Sci. École Norm. Sup. (4) 1977 441 472

[7] Casselman, W. Extended automorphic forms on the upper half plane Math. Ann. 1993 755 762

[8] Flicker, Yuval Z. Twisted tensors and Euler products Bull. Soc. Math. France 1988 295 313

[9] Flicker, Yuval Z. On distinguished representations J. Reine Angew. Math. 1991 139 172

[10] Flicker, Yuval Z. Distinguished representations and a Fourier summation formula Bull. Soc. Math. France 1992 413 465

[11] Flicker, Yuval Z., Hakim, Jeffrey L. Quaternionic distinguished representations Amer. J. Math. 1994 683 736

[12] Friedberg, Solomon, Jacquet, Hervã© Linear periods J. Reine Angew. Math. 1993 91 139

[13] Guo, Jiandong On the positivity of the central critical values of automorphic 𝐿-functions for 𝐺𝐿(2) Duke Math. J. 1996 157 190

[14] Harder, G., Langlands, R. P., Rapoport, M. Algebraische Zyklen auf Hilbert-Blumenthal-Flächen J. Reine Angew. Math. 1986 53 120

[15] Jacquet, Herv㩠Sur un résultat de Waldspurger Ann. Sci. École Norm. Sup. (4) 1986 185 229

[16] Jacquet, Herv㩠The continuous spectrum of the relative trace formula for 𝐺𝐿(3) over a quadratic extension Israel J. Math. 1995 1 59

[17] Jacquet, Hervã©, Lai, King F., Rallis, Stephen A trace formula for symmetric spaces Duke Math. J. 1993 305 372

[18] Jacquet, H., Lai, K. F. A relative trace formula Compositio Math. 1985 243 310

[19] Jacquet, Hervã©, Rallis, Stephen Symplectic periods J. Reine Angew. Math. 1992 175 197

[20] Jacquet, H., Shalika, J. A. On Euler products and the classification of automorphic representations. I Amer. J. Math. 1981 499 558

[21] Jacquet, Hervã©, Ye, Yangbo Une remarque sur le changement de base quadratique C. R. Acad. Sci. Paris Sér. I Math. 1990 671 676

[22] Lai, K. F. Algebraic cycles on compact Shimura surface Math. Z. 1985 593 602

[23] Lai, K. F. On Arthur’s class expansion of the relative trace formula Duke Math. J. 1991 111 117

[24] Langlands, R. P. Eisenstein series 1966 235 252

[25] Levy, Jason A note on the relative trace formula Canad. Math. Bull. 1995 450 461

[26] Laumon, Gã©Rard, Rapoport, Michael The Langlands lemma and the Betti numbers of stacks of 𝐺-bundles on a curve Internat. J. Math. 1996 29 45

[27] Mao, Zhengyu Relative Kloosterman integrals for the unitary group C. R. Acad. Sci. Paris Sér. I Math. 1992 381 386

[28] Må“Glin, Colette, Waldspurger, Jean-Loup Décomposition spectrale et séries d’Eisenstein 1994

[29] Sarnak, Peter C. Diophantine problems and linear groups 1991 459 471

[30] Springer, T. A. Some results on algebraic groups with involutions 1985 525 543

[31] Zagier, Don The Rankin-Selberg method for automorphic functions which are not of rapid decay J. Fac. Sci. Univ. Tokyo Sect. IA Math. 1981

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