P. Yatsyna

activity

20182026

most citedLifting problem for universal quadratic forms

33 citations · 92 across the 23 of their papers we have counts for

collaborators

25 papers

math.NT2026

Geometric bounds on norms of signed indecomposable integers

Siu Hang Man, Zdeněk Pezlar, Pavlo Yatsyna

We establish bounds on the norm of signed indecomposable integers in totally real number fields, via a geometric argument. We also improve the bound on the norm of totally positive…

math.NT2026

Height lower bounds for elements of highly composite rings

Siu Hang Man, Niclas Technau, Martin Widmer +1

Let $Q^{(d)}$ be the composite field of all number fields of degree at most $d$ . In 2001 Bombieri and Zannier proved that $Q^{(2)}$ has the Northcott property and…

math.NT2026

Lattice point sumsets and asymptotic approximate groups

Arindam Biswas, Pavlo Yatsyna

We establish new quantitative bounds for asymptotic approximate groups arising from finite subsets of lattices and, more generally, semi-linear subsets of abelian groups. Our appro…

math.NT2026

The Minimal Degree of Salem Numbers with Negative Trace

Subham Roy, Pavlo Yatsyna

We show that the minimal degree of a Salem number with prescribed negative trace is bounded below by $T^{2} / lo g T$ and above by $T^{2} lo g T$ , up to explicit constants and lower-order…

math.NT2025

Asymptotics of $n$ -universal lattices over number fields

Dayoon Park, Robin Visser, Pavlo Yatsyna +1

We prove an explicit asymptotic formula for the logarithm of the minimal ranks of $n$ -universal lattices over the ring of integers of totally real number fields. We also show that,…

math.NT2025

Counting polynomials with positive roots

Pavlo Yatsyna, Błażej Żmija

This paper investigates the number of monic integer polynomials of degree $n$ whose roots are all real and positive. We establish an asymptotic formula for the case of fixed trace…

math.NT2025

Pythagoras numbers for infinite algebraic fields

Nicolas Daans, Stevan Gajović, Siu Hang Man +1

We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…

math.NT2025

Additively indecomposable quadratic forms over totally real number fields

Magdaléna Tinková, Pavlo Yatsyna

We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real num…

math.NT2025

Kitaoka's Conjecture for quadratic fields

Vitezslav Kala, Jakub Krásenský, Dayoon Park +2

We prove that there are at most 13 real quadratic fields that admit a ternary universal quadratic lattice, thus establishing a strong version of Kitaoka's Conjecture for quadratic…

math.NT2024★ 1 cited

Most totally real fields do not have universal forms or Northcott property

Nicolas Daans, Vitezslav Kala, Siu Hang Man +2

We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott prope…

math.NT2024

Failures of integral Springer's Theorem

Nicolas Daans, Vítězslav Kala, Jakub Krásenský +1

We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this f…

math.NT2024

Even better sums of squares over quintic and cyclotomic fields

Vitezslav Kala, Pavlo Yatsyna

We classify all totally real number fields of degree at most 5 that admit a universal quadratic form with rational integer coefficients; in fact, there are none over the previously…

math.NT2023★ 4 cited

Real quadratic fields with a universal quadratic form of given rank have density zero

Vitezslav Kala, Pavlo Yatsyna, Błażej Żmija

We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More gene…

math.NT2023

There are Salem numbers with trace $- 3$ and every degree at least $34$

Giacomo Cherubini, Pavlo Yatsyna

We prove that there exist Salem numbers with trace $- 3$ and every even degree $\geq 34$ . Our proof combines a theoretical approach, which allows us to treat all sufficiently large…

math.NT2022

Potential energy of totally positive algebraic integers

Giacomo Cherubini, Pavlo Yatsyna

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant…

math.NT2021★ 9 cited

Consecutive real quadratic fields with large class numbers

Giacomo Cherubini, Alessandro Fazzari, Andrew Granville +2

For a given positive integer $k$ , we prove that there are at least $x^{1/2 - o (1)}$ integers $d \leq x$ such that the real quadratic fields $\mathbb Q(\sqrt{d+1}),\dots,\mathbb Q(\sqr…

math.NT2021★ 3 cited

On quadratic Waring's problem in totally real number fields

Jakub Krásenský, Pavlo Yatsyna

We improve the bound of the $g$ -invariant of the ring of integers of a totally real number field, where the $g$ -invariant $g (r)$ is the smallest number of squares of linear forms i…

math.NT2021★ 19 cited

On Kitaoka's conjecture and lifting problem for universal quadratic forms

Vítězslav Kala, Pavlo Yatsyna

For a totally positive definite quadratic form over the ring of integers of a totally real number field $K$ , we show that there are only finitely many totally real field extensions…

math.CO2021

Equiangular lines in Euclidean spaces: dimensions 17 and 18

Gary R. W. Greaves, Jeven Syatriadi, Pavlo Yatsyna

We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construct…

math.NT2020

Cyclic polytope of the simplest cubic fields

Giacomo Cherubini, Pavlo Yatsyna

In this paper, we study dilation of cyclic polytopes with the vertices defined by a generator of the simplest cubic fields. In particular, for a specific range of values, we give a…

math.NT2020★ 2 cited

Sums of squares in $S$ -integers

Vítězslav Kala, Pavlo Yatsyna

In totally real number fields, we characterize the rings of $S$ -integers (obtained by inverting a rational integer $m$ ) such that all their totally positive elements are represente…

math.CO2020

Equiangular lines in low dimensional Euclidean spaces

Gary R. W. Greaves, Jeven Syatriadi, Pavlo Yatsyna

We show that the maximum cardinality of an equiangular line system in 14 and 16 dimensions is 28 and 40, respectively, thereby solving a longstanding open problem. We also improve…

math.NT2018★ 1 cited

A lower bound for the rank of a universal quadratic form with integer coefficients in a totally real number field

Pavlo Yatsyna

We show that if $K$ is a monogenic, primitive, totally real number field, that contains units of every signature, then there exists a lower bound for the rank of integer universal…

math.NT2018★ 33 cited

Lifting problem for universal quadratic forms

Vítězslav Kala, Pavlo Yatsyna

We study totally real number fields that admit a universal quadratic form whose coefficients are rational integers. We show that $Q (5)$ is the only such real quadrati…

Geometric bounds on norms of signed indecomposable integers

Height lower bounds for elements of highly composite rings

Lattice point sumsets and asymptotic approximate groups

The Minimal Degree of Salem Numbers with Negative Trace

Asymptotics of n-universal lattices over number fields

Counting polynomials with positive roots

Pythagoras numbers for infinite algebraic fields

Additively indecomposable quadratic forms over totally real number fields

Kitaoka's Conjecture for quadratic fields

Most totally real fields do not have universal forms or Northcott property

Failures of integral Springer's Theorem

Even better sums of squares over quintic and cyclotomic fields

Real quadratic fields with a universal quadratic form of given rank have density zero

There are Salem numbers with trace −3 and every degree at least 34

Potential energy of totally positive algebraic integers

Consecutive real quadratic fields with large class numbers

On quadratic Waring's problem in totally real number fields

On Kitaoka's conjecture and lifting problem for universal quadratic forms

Equiangular lines in Euclidean spaces: dimensions 17 and 18

Cyclic polytope of the simplest cubic fields

Sums of squares in S-integers

Equiangular lines in low dimensional Euclidean spaces

A lower bound for the rank of a universal quadratic form with integer coefficients in a totally real number field

Lifting problem for universal quadratic forms

Asymptotics of $n$ -universal lattices over number fields

There are Salem numbers with trace $- 3$ and every degree at least $34$

Sums of squares in $S$ -integers