Geodesic
$K$-finite Whittaker functions are of finite order one
Acta Arithmetica, Tome 158 (2013) no. 4, pp. 359-401

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathbb {C}^n$, 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.
DOI : 10.4064/aa158-4-4
Keywords: prove finite order type estimate whittaker function attached k finite section principle series representation real complex chevalley group effective computations made using convexity mathbb following original paper jacquet application simplified proof known result boundedness vertical strips certain automorphic l functions using result ller

Mark McKee 1

1 
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Mark McKee. $K$-finite Whittaker functions are of finite order one. Acta Arithmetica, Tome 158 (2013) no. 4, pp. 359-401. doi: 10.4064/aa158-4-4

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