A. Bondarenko

collaborators

7 papers

math.NT2026

Siegel zeros and small gaps between zeros of the Riemann zeta function

Andriy Bondarenko, Winston Heap

On assuming the Riemann Hypothesis, we show that Siegel zeros imply the existence of gaps between the zeros of the Riemann zeta function less than 1/2 the normalised length. Specif…

math.MG2026

On GrÃ¼nbaum's problem for symmetric configurations

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

Let $g_{n}$ be the largest number of Euclidean balls of diameter $1$ which may be needed to cover a set of diameter $1$ in $R^{n}$ . We study this problem for finite sets invar…

math.CO2026

A construction of spherical $5$ -designs with $O (d^{2})$ points

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

For every $d \geq 1$ we give an explicit equal-weight spherical $5$ -design in $S^{d - 1} \subset R^{d}$ with at most $72 d^{2}$ points. Our approach utilizes recent construc…

math.NT2025

The basis functions of Fourier interpolation

David Berghaus, Andriy Bondarenko, Danylo Radchenko +2

The basis functions of the Fourier interpolation formula of Radchenko and Viazovska, constructed by means of weakly holomorphic modular forms for the Hecke theta group, are entire…

math.MG2025

Small Volume Bodies of Constant Width with Tetrahedral Symmetries

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

For every $n \geq 2$ , we construct a body $U_{n}$ of constant width $2$ in $E^{n}$ with small volume and symmetries of a regular $n$ -simplex. $U_{2}$ is the Reuleaux triangle. To…

math.MG2025

On asymptotic Lebesgue's universal covering problem

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

Universal cover in $E^{n}$ is a measurable set that contains a congruent copy of any set of diameter 1. Lebesgue's universal covering problem, posed in 1914, asks for the…

Siegel zeros and small gaps between zeros of the Riemann zeta function

On GrÃ¼nbaum's problem for symmetric configurations

A construction of spherical 5-designs with O(d2) points

The basis functions of Fourier interpolation

Small Volume Bodies of Constant Width with Tetrahedral Symmetries

On asymptotic Lebesgue's universal covering problem

A construction of spherical $5$ -designs with $O (d^{2})$ points