We prove a finite order one type estimate for the Whittaker function attached to a K-finite section of a principle series representation of a real or complex Chevalley group. Effective computations are made using convexity in ℂⁿ, following the original paper of Jacquet. As an application, we give a simplified proof of the known result of the boundedness in vertical strips of certain automorphic L-functions, using a result of Müller.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-4-4,
title = {K-finite Whittaker functions are of finite order one},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {359-401},
zbl = {1307.11061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-4-4}
}
(éd.). K-finite Whittaker functions are of finite order one. Acta Arithmetica, Tome 161 (2013) pp. 359-401. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa158-4-4/