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, 22E45, 41A60, 11M99, 30D15, 33C15 show english descriptions Representation-theoretic methods; automorphic representations over local and global fields
Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
None of the above, but in this section
Special classes of entire functions and growth estimates
Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$ 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, ${}_1F_1$

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