K-finite Whittaker functions are of finite order one

• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 33C15: Confluent hypergeometric functions, Whittaker functions, 1 F 1
• 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods
• 11F70: Representation-theoretic methods; automorphic representations over local and global fields
• 30D15: Special classes of entire functions and growth estimates
• 11M99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 4
• Strony: 359-401

Daty

wydano

2013

Twórcy

Identyfikatory

DOI

10.4064/aa158-4-4