PreprintCC BY 4.0arXiv
Norms of Schneider--Teitelbaum Polynomials in p-adic Fourier Theory
Abstract
Let F be the unramified quadratic extension of ℚp, and let Pn(T) denote the polynomials arising in the p-adic Fourier theory of Schneider and Teitelbaum. We determine explicitly the norms of the functions Pn(xΩ) on the Banach spaces of locally F-analytic functions of fixed order, where Ω is a Lubin--Tate period. Our computation is based on a recent valuation formula of Ardakov and Berger for the values Pn(Ω). As an application, we obtain an explicit normalization of the basis constructed by Bannai and Kobayashi, whose elements all have norm one.
Related
- Density of polynomials whose Aron--Berner extensions attain their norms
- Cyclic Kronecker Fourier Transforms, Weber Norms, and Rogers-Ramanujan Singular Values
- Quartic Fourier-Laplace limits for (p,q)-Rogers-Szegő polynomials
- Fourier Decomposition and E-Eigenvalues of Hypergraph Polynomials over Finite Abelian Groups
- Universal norms of partially de Rham B-pairs and perfectness in Lubin--Tate Iwasawa theory
BibTeX
@misc{katagiri2026norms,
title = {{Norms of Schneider--Teitelbaum Polynomials in $p$-adic Fourier Theory}},
author = {Yu Katagiri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20002},
eprint = {2609.20002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20002},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Norms of Schneider--Teitelbaum Polynomials in p-adic Fourier Theory
AU - Yu Katagiri
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20002
UR - https://arxiv.org/abs/2609.20002
AB - Let F be the unramified quadratic extension of ℚ_p, and let P_n(T) denote the polynomials arising in the p-adic Fourier theory of Schneider and Teitelbaum. We determine explicitly the norms of the functions P_n(xΩ) on the Banach spaces of locally F-analytic functions of fixed order, where Ω is a Lubin--Tate period. Our computation is based on a recent valuation formula of Ardakov and Berger for the values P_n(Ω). As an application, we obtain an explicit normalization of the basis constructed by Bannai and Kobayashi, whose elements all have norm one.
ER -