Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.28477

Counting Bessel zeros and applications

Gal Binyamini·Avner Kiro·Gady Kozma·Jonathan Pila
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.CAmath.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gal Binyamini, Avner Kiro, Gady Kozma, Jonathan Pila. 2026-10-20. Counting Bessel zeros and applications. https://arxiv.org/abs/2610.28477

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation

We generalized the mKdV equation in order that the static equations include ${\rm sn}$ differential equation. As a result, a good correspondence was obtained between the KdV equation and the mKdV equation.For general genus two hyperelliptic curves, we obtained differential equations for Weierstrass type and Jacobi type hyperelliptic functions. Considering the special case of $λ_6=0, λ_0=0$, Weierstrass type and Jacobi type hyperelliptic functions are different solutions to the same hyperelliptic differential equations. Then these solutions are connected by the special ${\rm Sp(4, {\bf R})}$ Lie group transformation.

math.CA↗
arXiv2026

Lifting curved Kakeya sets to linear Kakeya sets

We prove that many curved Kakeya problems, originally motivated by Hörmander's oscillatory integral problem, lift to the classical Kakeya problem in higher dimensions. As a consequence, if the classical Kakeya set conjecture were true in all dimensions, the families of curves whose curved Kakeya sets have full dimension are dense among Hörmander-type families. This is in contrast to the nowhere dense Bourgain's condition, which is a necessary condition for best-case curved Kakeya maximal function estimates. Furthermore the linear Kakeya set conjecture would imply a fairly complete understanding of Kakeya sets of quadratic curves, as first studied systematically by Wisewell. These results give a better understanding of a question posed by Guo--Guth--Nadjimzadah--Shen--Zhang, and they more generally show that the classical Kakeya conjecture in high dimensions rests on a broad range of curved Kakeya problems in lower dimensions.

math.CA↗
arXiv2026

Jackson and Bernstein Inequalities with Explicit Weight Dependence for Band-Limited Wavelet Approximation in Weighted Besov Spaces

We prove direct and inverse estimates for band-limited biorthogonal wavelet systems in weighted Besov spaces with Muckenhoupt weights. On functions recovered from their wavelet expansion along the dyadic tree of the unit cube, the error of approximation by a prescribed number of terms decays at a rate set by the smoothness-to-dimension ratio, and this exponent cannot be increased. Under a multiresolution condition, Bernstein inequalities hold at a single scale and on every multiresolution subspace, and the linear approximation spaces are identified with weighted Lebesgue--Besov intersections. All constants are explicit; the weight enters only through displayed powers of the Muckenhoupt characteristic.

math.CA↗