Cuspidality of symmetric powers with applications
Kim, Henry H. ; Shahidi, Freydoon
Duke Math. J., Tome 115 (2002) no. 1, p. 177-197 / Harvested from Project Euclid
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The purpose of this paper is to prove that the symmetric fourth power of a cusp form on ${\rm GL}(2)$, whose existence was proved earlier by the first author, is cuspidal unless the corresponding automorphic representation is of dihedral, tetrahedral, or octahedral type. As a consequence, we prove a number of results toward the Ramanujan-Petersson and Sato-Tate conjectures. In particular, we establish the bound $q\sp {1/9}\sb v$ for unramified Hecke eigenvalues of cusp forms on ${\rm GL}(2)$. Over an arbitrary number field, this is the best bound available at present.
Publié le : 2002-03-15
Classification:  11F70,  11F30,  11R42 
@article{1087575125,
     author = {Kim, Henry H. and Shahidi, Freydoon},
     title = {Cuspidality of symmetric powers with applications},
     journal = {Duke Math. J.},
     volume = {115},
     number = {1},
     year = {2002},
     pages = { 177-197},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087575125}
}

Kim, Henry H.; Shahidi, Freydoon. Cuspidality of symmetric powers with applications. Duke Math. J., Tome 115 (2002) no. 1, pp.  177-197. http://gdmltest.u-ga.fr/item/1087575125/