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PreprintCC BY 4.0arXiv

Bounds on Whittaker Functions for GL(n)

  • Gilles Felber
  • Dávid Tóth
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Abstract

We prove a new estimate on Jacquet-Whittaker function for GLn(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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Cite

BibTeXRIS
BibTeX
@misc{felber2026bounds,
  title = {{Bounds on Whittaker Functions for $\mathrmGL(n)$}},
  author = {Gilles Felber and Dávid Tóth},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06501},
  eprint = {2609.06501},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06501},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bounds on Whittaker Functions for GL(n)
AU  - Gilles Felber
AU  - Dávid Tóth
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06501
UR  - https://arxiv.org/abs/2609.06501
AB  - We prove a new estimate on Jacquet-Whittaker function for GL_n(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.
ER  -