Geodesic
A new tower of Rankin-Selberg integrals
Ginzburg, David1 ; Hundley, Joseph2
1 School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
2 Mathematics Department, Penn State University, University Park, PA 16802
Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 56-62 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

We recall the notion of a tower of Rankin-Selberg integrals, and two known towers, making observations of how the integrals within a tower may be related to one another via formal manipulations, and offering a heuristic for how the $L$-functions should be related to one another when the integrals are related in this way. We then describe three new integrals in a tower on the group $E_6,$ and find out which $L$-functions they represent. The heuristics also predict the existence of a fourth integral.
DOI : 10.1090/S1079-6762-06-00160-0

Ginzburg, David 1 ; Hundley, Joseph 2

1 School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
2 Mathematics Department, Penn State University, University Park, PA 16802 
@article{10_1090_S1079_6762_06_00160_0,
     author = {Ginzburg, David and Hundley, Joseph},
     title = {A new tower of {Rankin-Selberg} integrals},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {56--62},
     year = {2006},
     volume = {12},
     doi = {10.1090/S1079-6762-06-00160-0},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-06-00160-0/}
}
TY  - JOUR
AU  - Ginzburg, David
AU  - Hundley, Joseph
TI  - A new tower of Rankin-Selberg integrals
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2006
SP  - 56
EP  - 62
VL  - 12
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-06-00160-0/
DO  - 10.1090/S1079-6762-06-00160-0
ID  - 10_1090_S1079_6762_06_00160_0
ER  - 
%0 Journal Article
%A Ginzburg, David
%A Hundley, Joseph
%T A new tower of Rankin-Selberg integrals
%J Electronic research announcements of the American Mathematical Society
%D 2006
%P 56-62
%V 12
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-06-00160-0/
%R 10.1090/S1079-6762-06-00160-0
%F 10_1090_S1079_6762_06_00160_0
Ginzburg, David; Hundley, Joseph. A new tower of Rankin-Selberg integrals. Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 56-62. doi: 10.1090/S1079-6762-06-00160-0

[1] Gelbart, Stephen, Jacquet, Hervé A relation between automorphic representations of 𝐺𝐿(2) and 𝐺𝐿(3) Ann. Sci. École Norm. Sup. (4) 1978 471 542

[2] Ginzburg, David A Rankin-Selberg integral for the adjoint representation of 𝐺𝐿₃ Invent. Math. 1991 571 588

[3] Ginzburg, David On standard 𝐿-functions for 𝐸₆ and 𝐸₇ J. Reine Angew. Math. 1995 101 131

[4] Ginzburg, David, Jiang, Dihua Periods and liftings: from 𝐺₂ to 𝐶₃ Israel J. Math. 2001 29 59

[5] Ginzburg, D., Rallis, S. A tower of Rankin-Selberg integrals Internat. Math. Res. Notices 1994

[6] Ginzburg, David, Rallis, Stephen, Soudry, David On the automorphic theta representation for simply laced groups Israel J. Math. 1997 61 116

[7] Jacquet, Hervé, Shalika, Joseph Exterior square 𝐿-functions 1990 143 226

[8] Kac, V. G. Some remarks on nilpotent orbits J. Algebra 1980 190 213

[9] Shahidi, Freydoon On certain 𝐿-functions Amer. J. Math. 1981 297 355

Cité par Sources :