PreprintCC BY 4.0arXiv
On the uniform flatness of polynomial graphs
Abstract
This paper grew out of an effort to understand the so-called uniform flatness, an important concept in the Bargmann--Fock interpolation theory developed by Varolin et al. We show that the graph of every polynomial in one complex variable is a uniformly flat algebraic curve in ℂ2, with vanishing upper density with respect to the Gaussian weight. Combined with a result of Pingali and Varolin, this implies that such graphs are interpolating for the Bargmann--Fock space on ℂ2.
Versions
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BibTeX
@misc{wang2026uniform,
title = {{On the uniform flatness of polynomial graphs}},
author = {Xieping Wang and Li Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15599},
eprint = {2609.15599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15599},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the uniform flatness of polynomial graphs
AU - Xieping Wang
AU - Li Zhang
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15599
UR - https://arxiv.org/abs/2609.15599
AB - This paper grew out of an effort to understand the so-called uniform flatness, an important concept in the Bargmann--Fock interpolation theory developed by Varolin et al. We show that the graph of every polynomial in one complex variable is a uniformly flat algebraic curve in ℂ^2, with vanishing upper density with respect to the Gaussian weight. Combined with a result of Pingali and Varolin, this implies that such graphs are interpolating for the Bargmann--Fock space on ℂ^2.
ER -