Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 2 (2017), 325-402.
Level-raising and symmetric power functoriality, III
The simplest case of the Langlands functoriality principle asserts the existence of the symmetric powers of a cuspidal representation of over the adèles of , where is a number field. In 1978, Gelbart and Jacquet proved the existence of . After this, progress was slow, eventually leading, through the work of Kim and Shahidi, to the existence of and . In this series of articles we revisit this problem using recent progress in the deformation theory of modular Galois representations. As a consequence, our methods apply only to classical modular forms on a totally real number field; the present article proves the existence, in this “classical” case, of and .
Duke Math. J., Volume 166, Number 2 (2017), 325-402.
Received: 17 July 2014
Revised: 10 December 2015
First available in Project Euclid: 9 December 2016
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Clozel, Laurent; Thorne, Jack A. Level-raising and symmetric power functoriality, III. Duke Math. J. 166 (2017), no. 2, 325--402. doi:10.1215/00127094-3714971. https://projecteuclid.org/euclid.dmj/1481252669