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K-finite Whittaker functions are of finite order one

(2013)

Acta Arithmetica

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.

Krätzel Function as a Function of Hypergeometric Type

Kilbas, Anatoly, Saxena, R. K., Trujillo, Juan (2006)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15The paper is devoted to the study of the function Zνρ(x) defined for positive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0 for ρ ≤ 0, [...] Such a function was earlier investigated for ρ > 0. Using the Mellin transform of Zνρ(x), we establish its representations in terms of the H-function and extend this function from positive x > 0 to complex z. The results obtained, being different for ρ > 0 and ρ <...

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