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Corners with polynomial side length
Noah Kravitz, Borys Kuca, James Leng
A -polynomial corner, for a polynomial, is a triple of points for . In the case where has an…
Quantitative concatenation for polynomial box norms
Noah Kravitz, Borys Kuca, James Leng
Using PET and quantitative concatenation techniques, we establish box-norm control with the "expected" directions for counting operators for general multidimensional polynomial pro…
Multidimensional polynomial patterns over finite fields: bounds, counting estimates and Gowers norm control
Borys Kuca
We examine multidimensional polynomial progressions involving linearly independent polynomials in finite fields, proving power saving bounds for sets lacking such configurations. T…
True complexity of polynomial progressions in finite fields
Borys Kuca
The true complexity of a polynomial progression in finite fields corresponds to the smallest-degree Gowers norm that controls the counting operator of the progression over finite f…