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arXiv · 2609.19121

The non-spherical sup-norm problem for $\mathrm{GL}(n)$ and generalized spherical functions

Valentin Blomer·Gergely Harcos·Péter Maga·Djordje Milićević
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Abstract

We solve the sup-norm problem for minimal weight vectors in an arbitrary cuspidal representation $π$ of $\mathrm{GL}(n,\mathbb{Z})\backslash\mathrm{GL}(n,\mathbb{R})$ with a uniform power saving bound in terms of the archimedean data of $π$, including its spectral parameters and the dimension of its minimal $K$-type. As a key ingredient, we establish new uniform decay bounds for generalized spherical functions.

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Valentin Blomer, Gergely Harcos, Péter Maga, Djordje Milićević. 2026-09-16. The non-spherical sup-norm problem for $\mathrm{GL}(n)$ and generalized spherical functions. https://arxiv.org/abs/2609.19121

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