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# An Infinite Order Whittaker Function

Published:2009-04-01
Printed: Apr 2009
• Mark McKee
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## Abstract

In this paper we construct a flat smooth section of an induced space $I(s,\eta)$ of $SL_2(\mathbb{R})$ so that the attached Whittaker function is not of finite order. An asymptotic method of classical analysis is used.
 MSC Classifications: 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 22E45 - Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05} 41A60 - Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 11M99 - None of the above, but in this section 30D15 - Special classes of entire functions and growth estimates 33C15 - Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$