PreprintCC0arXiv
Comment on "Landau Levels and Riemann Zeros"
Abstract
Sierra and Townsend (ST) [1] showed that the ``absorption spectrum'' model of Connes [2] arises as the lowest-Landau-level (LLL) limit of a charged particle in crossed electric and magnetic fields, and suggested that the higher Landau levels supply the fluctuation part of the Riemann-zero counting function N(E). Within the approximation used by ST we construct the eigenfunctions of an arbitrary Landau level n and derive their asymptotics at the two box boundaries that ST identify. The boundary condition is the same as for n=0 up to an E-independent phase (−ii)n, so no ln E term arises for any fixed n. We also note that the ln E term in the semiclassical Eq.~(29) of ST is the first-order shift of the smooth LLL counting function, E→ E+γz2.
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BibTeX
@misc{hwang2026comment,
title = {{Comment on "Landau Levels and Riemann Zeros"}},
author = {Mi-Ra Hwang and Eylee Jung and MuSeong Kim and DaeKil Park},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14108},
eprint = {2610.14108},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14108},
note = {CC0},
}
RIS
TY - UNPB
TI - Comment on "Landau Levels and Riemann Zeros"
AU - Mi-Ra Hwang
AU - Eylee Jung
AU - MuSeong Kim
AU - DaeKil Park
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.14108
UR - https://arxiv.org/abs/2610.14108
AB - Sierra and Townsend (ST) [1] showed that the ``absorption spectrum'' model of Connes [2] arises as the lowest-Landau-level (LLL) limit of a charged particle in crossed electric and magnetic fields, and suggested that the higher Landau levels supply the fluctuation part of the Riemann-zero counting function N(E). Within the approximation used by ST we construct the eigenfunctions of an arbitrary Landau level n and derive their asymptotics at the two box boundaries that ST identify. The boundary condition is the same as for n=0 up to an E-independent phase (−ii)^n, so no ln E term arises for any fixed n. We also note that the ln E term in the semiclassical Eq.~(29) of ST is the first-order shift of the smooth LLL counting function, E→ E+γz^2.
ER -