A. Bondarenko

activity

20152026

most citedSpherical coverings and X-raying convex bodies of constant width

4 citations · 6 across the 12 of their papers we have counts for

collaborators

13 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 Grünbaum'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

On asymptotic Lebesgue's universal covering problem

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

A 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 th…

math.MG2024

On a Gallai-type problem and illumination of spiky balls and cap bodies

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

We show that any finite family of pairwise intersecting balls in $E^{n}$ can be pierced by $(3/2 + o (1))^{n}$ points improving the previously known estimate of $(2+o(1))^…

math.MG2024

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.MG2024★ 1 cited

Small volume bodies of constant width

Andrii Arman, Andriy Bondarenko, Fedor Nazarov +2

For every large enough $n$ , we explicitly construct a body of constant width $2$ that has volume less than $0. 9^{n} Vol (B^{n}$ ), where $B^{n}$ is the unit ba…

math.MG2024

On Hadwiger's covering problem in small dimensions

Andrii Arman, Andriy Bondarenko, Andriy Prymak

Let $H_{n}$ be the minimal number such that any $n$ -dimensional convex body can be covered by $H_{n}$ translates of interior of that body. Similarly $H_{n}^{s}$ is the corresponding quanti…

math.MG2023

Convex bodies of constant width with exponential illumination number

Andrii Arman, Andriy Bondarenko, Andriy Prymak

We show that there exist convex bodies of constant width in $E^{n}$ with illumination number at least $(cos (π /14) + o (1))^{- n}$ , answering a question by G. Kalai. Furthermore…

math.CO2021★ 1 cited

Upper bounds on chromatic number of $E^{n}$ in low dimensions

Andrii Arman, Andriy V. Bondarenko, Andriy Prymak +1

Let $χ (E^{n})$ denote the chromatic number of the Euclidean space $E^{n}$ , i.e., the smallest number of colors that can be used to color $E^{n}$ so that no two…

math.MG2020★ 4 cited

Spherical coverings and X-raying convex bodies of constant width

A. Bondarenko, A. Prymak, D. Radchenko

K. Bezdek and Gy. Kiss showed that existence of origin-symmetric coverings of unit sphere in $E^{n}$ by at most $2^{n}$ congruent spherical caps with radius not exceeding $\ar…

math.CO2015

There is no strongly regular graph with parameters (460,153,32,60)

A. V. Bondarenko, A. Mellit, A. Prymak +2

We prove that there is no strongly regular graph (SRG) with parameters (460,153,32,60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some appl…

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

On Grünbaum's problem for symmetric configurations

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

The basis functions of Fourier interpolation

On asymptotic Lebesgue's universal covering problem

On a Gallai-type problem and illumination of spiky balls and cap bodies

Small Volume Bodies of Constant Width with Tetrahedral Symmetries

Small volume bodies of constant width

On Hadwiger's covering problem in small dimensions

Convex bodies of constant width with exponential illumination number

Upper bounds on chromatic number of En in low dimensions

Spherical coverings and X-raying convex bodies of constant width

There is no strongly regular graph with parameters (460,153,32,60)

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

Upper bounds on chromatic number of $E^{n}$ in low dimensions