PreprintCC BY 4.0arXiv
Counting Bessel zeros and applications
Abstract
We establish o-minimal definability results and develop point-counting machinery applicable to the zeros of a Bessel function of fixed non-negative real parameter. We also give an Ax-Schanuel theorem for Bessel functions of fixed (complex) parameters and exponential functions. We combine these to prove a sparsity result (weak Manin-Mumford) for points on an algebraic variety whose coordinates are zeros of a Bessel function of fixed (non-negative real) parameter. We apply this result to improve density results on spectral sets for the unit ball motivated by Fuglede's conjecture.
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BibTeX
@misc{binyamini2026counting,
title = {{Counting Bessel zeros and applications}},
author = {Gal Binyamini and Avner Kiro and Gady Kozma and Jonathan Pila},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28477},
eprint = {2610.28477},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28477},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Counting Bessel zeros and applications
AU - Gal Binyamini
AU - Avner Kiro
AU - Gady Kozma
AU - Jonathan Pila
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28477
UR - https://arxiv.org/abs/2610.28477
AB - We establish o-minimal definability results and develop point-counting machinery applicable to the zeros of a Bessel function of fixed non-negative real parameter. We also give an Ax-Schanuel theorem for Bessel functions of fixed (complex) parameters and exponential functions. We combine these to prove a sparsity result (weak Manin-Mumford) for points on an algebraic variety whose coordinates are zeros of a Bessel function of fixed (non-negative real) parameter. We apply this result to improve density results on spectral sets for the unit ball motivated by Fuglede's conjecture.
ER -