PreprintarXiv licencearXiv
The non-spherical sup-norm problem for GL(n) and generalized spherical functions
Abstract
We solve the sup-norm problem for minimal weight vectors in an arbitrary cuspidal representation π of GL(n,ℤ)backslashGL(n,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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BibTeX
@misc{blomer2026nonspherical,
title = {{The non-spherical sup-norm problem for $\mathrmGL(n)$ and generalized spherical functions}},
author = {Valentin Blomer and Gergely Harcos and Péter Maga and Djordje Milićević},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19121},
eprint = {2609.19121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19121},
}
RIS
TY - UNPB
TI - The non-spherical sup-norm problem for GL(n) and generalized spherical functions
AU - Valentin Blomer
AU - Gergely Harcos
AU - Péter Maga
AU - Djordje Milićević
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19121
UR - https://arxiv.org/abs/2609.19121
AB - We solve the sup-norm problem for minimal weight vectors in an arbitrary cuspidal representation π of GL(n,ℤ)backslashGL(n,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.
ER -