Functorial products for $GL_2\times GL_3$ and the symmetric cube for $GL_2$
| dc.creator | Kim, Henry H. | |
| dc.creator | Shahidi, Freydoon | |
| dc.creator | Bushnell, Colin J. | |
| dc.creator | Henniart, Guy | |
| dc.date | 2004-09-30 | |
| dc.date.accessioned | 2026-07-07T12:50:36Z | |
| dc.date.available | 2026-07-07T12:50:36Z | |
| dc.description | In this paper we prove two new cases of Langlands functoriality. The first is a functorial product for cusp forms on $GL_2\times GL_3$ as automorphic forms on $GL_6$, from which we obtain our second case, the long awaited functorial symmetric cube map for cusp forms on $GL_2$. We prove these by applying a recent version of converse theorems of Cogdell and Piatetski-Shapiro to analytic properties of certain $L$-functions obtained from the method of Eisenstein series (Langlands-Shahidi method). As a consequence, we prove the bound 5/34 for Hecke eigenvalues of Maass forms over any number field and at every place, finite or infinite, breaking the crucial bound 1/6 (see below and Section 7 and 8) towards Ramanujan-Petersson and Selberg conjectures for $GL_2$. Many other applications are obtained. | |
| dc.description | 57 pages, published version. Appendix by Colin J. Bushnell and Guy Henniart | |
| dc.identifier | https://arxiv.org/abs/math/0409607 | |
| dc.identifier | http://arxiv.org/abs/math/0409607 | |
| dc.identifier | Ann. of Math. (2), Vol. 155 (2002), no. 3, 837--893 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222733 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.title | Functorial products for $GL_2\times GL_3$ and the symmetric cube for $GL_2$ | |
| dc.type | text |