Evaluating Jacquet’s 𝐆𝐋(𝐧) Whittaker function

Broughan, Kevin

doi:10.1090/S0025-5718-08-02158-3

Evaluating Jacquet’s $\mathbf {\textrm {GL}(n)}$ Whittaker function
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by Kevin A. Broughan PDF

Math. Comp. 78 (2009), 1061-1072 Request permission

Abstract:

Algorithms for the explicit symbolic and numeric evaluation of Jacquet’s Whittaker function for the $GL(n,\mathbb {R})$ based generalized upper half-plane for $n\ge 2$, and an implementation for symbolic evaluation in the Mathematica package GL(n)pack, are described. This requires a comparison of the different definitions of Whittaker function which have appeared in the literature.

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