$K$-finite Whittaker functions are of finite order one

Volume 158 / 2013

Mark McKee Acta Arithmetica 158 (2013), 359-401 MSC: Primary 11F70, 22E45, 33C15; Secondary 11M99, 30D15. DOI: 10.4064/aa158-4-4


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.


Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image