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arXiv · 2609.06501

Bounds on Whittaker Functions for $\mathrm{GL}(n)$

Gilles Felber·Dávid Tóth
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Abstract

We prove a new estimate on Jacquet-Whittaker function for $\mathrm{GL}_n(\mathbb R)$, assuming that the Langlands parameters are purely imaginary and well-spaced. This gives an upper bound for the global sup-norm of the Whittaker function that matches the lower bound of Brumley-Templier in the exponent up to a linear error in $n$.

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Gilles Felber, Dávid Tóth. 2026-09-06. Bounds on Whittaker Functions for $\mathrm{GL}(n)$. https://arxiv.org/abs/2609.06501

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