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P-adic s-energy and Fourier dimension
Abstract
We extend the theory of s-energy to ℚpn. We give an exact representation for the s-energy in terms of the Fourier coefficients of a finite Borel measure with support in ℤpn, which is stronger than the approximate representation in ℝn. We also compute the Fourier dimension of the p-adic Riesz product measure, even in the case p=2, which has never been studied before.
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BibTeX
@misc{liu2026padic,
title = {{$P$-adic $s$-energy and Fourier dimension}},
author = {Cheng Liu and Lingmin Liao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22881},
eprint = {2609.22881},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22881},
}
RIS
TY - UNPB
TI - P-adic s-energy and Fourier dimension
AU - Cheng Liu
AU - Lingmin Liao
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.22881
UR - https://arxiv.org/abs/2609.22881
AB - We extend the theory of s-energy to ℚ_p^n. We give an exact representation for the s-energy in terms of the Fourier coefficients of a finite Borel measure with support in ℤ_p^n, which is stronger than the approximate representation in ℝ^n. We also compute the Fourier dimension of the p-adic Riesz product measure, even in the case p=2, which has never been studied before.
ER -