$p$-adic zeta integrals on unitary groups via Bushnell-Kutzko types

David Marcil

$p$-adic zeta integrals on unitary groups via Bushnell-Kutzko types

Number Theory 2023-11-13 v2

Authors: David Marcil

Abstract

In this paper, we compute certain $p$ -adic zeta integrals appearing in the doubling method of Garrett and Piatetski-Shapiro-Rallis for unitary groups. Using structure theorems in the author's work arXiv:2310.09110 for $P$ -(anti-)ordinary automorphic representations involving Bushnell-Kutzko types, we associate local Siegel-Weil sections at $p$ to such Bushnell-Kutzko types. Then, fixing compatible choices of $P$ -anti-ordinary vectors, we find explicit formulae relating the corresponding $p$ -adic zeta integral to modified $p$ -Euler factors and volumes of $P$ -Iwahoric subgroups. Our results extend the ones of Eischen, Harris, Li and Skinner for the ordinary setting by allowing automorphic representations with nontrivial supercuspidal support at $p$ .

Keywords

p-adic zeta integrals unitary groups doubling method bushnell-kutzko types siegel-weil sections p-ordinary representations iwahoric subgroups

Cite

@article{arxiv.2311.05466,
  title  = {$p$-adic zeta integrals on unitary groups via Bushnell-Kutzko types},
  author = {David Marcil},
  journal= {arXiv preprint arXiv:2311.05466},
  year   = {2023}
}

Comments

31 pages. Corrected various typos. The most important one involved the definition of the matrix coefficients introduced in Section 3.2.1

$p$-adic zeta integrals on unitary groups via Bushnell-Kutzko types

Abstract

Keywords

Cite

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