arXiv subjects

Bartosz Głowacki

Publications and source records attributed to Bartosz Głowacki.

2 recordsLinked to original sources

arXiv2026

Further bounds in the polynomial Szemerédi theorem

We show that there exists $c > 0$ such that any subset of $\{1,\ldots,N\}$ having size $\gg N / \exp( (\log\log\log N)^c )$ contains a nontrivial pattern of the form $x,x+y,x+2y,x+y^3$. It is the first configuration of complexity strictly greater than $0$, other than refinements of arithmetic progressions, for which quantitative bounds over integers were obtained.

math.NT↗

arXiv2026

Sums of squares on curves and surfaces

We study sums of higher even powers in the coordinate rings of singular planar curves $x^M=y^m$ for coprime positive integers $m 1$, can be of codimension $2$, contrary to the quadratic case.

math.AC↗