L. Mili'cevi'c

activity

20242026

collaborators

6 papers

math.CO2026

General inverse theory for the $U^{4}$ norm

Luka MiliÄeviÄ

In this paper, we develop a quantitative inverse theory for the Gowers uniformity norm $∥ \cdot ∥_{U^{4}}$ in general finite abelian groups. We identify a new type of obstru…

math.CO2025

MÃ¶bius function is strongly orthogonal to polynomial phases over $F_{p} [t]$

Luka MiliÄeviÄ, Å½arko RanÄeloviÄ

In this paper, we prove power-saving bounds for the corelation of the MÃ¶bius function with polynomial phases of degree $k$ in function fields $F_{p} [t]$ , when $p > k$ . The…

math.CO2025

Low-codimensional Subvarieties Inside Dense Multilinear Varieties

Luka MiliÄeviÄ

Let $G_{1}, \dots, G_{k}$ be finite-dimensional vector spaces over a prime field $F_{p}$ . Let $V$ be a variety inside $G_{1} \times \dots \times G_{k}$ defined by a multilinear map…

math.CO2024

A Bilinear Bogolyubov Argument in Abelian Groups

L. MiliÄeviÄ

The bilinear Bogolyubov argument for $F_{p}^{n}$ states that if we start with a dense set $A \subseteq F_{p}^{n} \times F_{p}^{n}$ and carry out sufficiently many st…

math.CO2024

Quasipolynomial inverse theorem for the $U^{4} (F_{p}^{n})$ norm

Luka MiliÄeviÄ

The inverse theory for Gowers uniformity norms is one of the central topics in additive combinatorics and one of the most important aspects of the theory is the question of bounds.…

math.CO2024

Good bounds for sets lacking skew corners

Luka MiliÄeviÄ

A skew corner is a triple of points in $Z \times Z$ of the form $(x, y), (x, y + a)$ and $(x + a, y^{'})$ . Pratt posed the following question: how large can a set $A…

General inverse theory for the U4 norm

MÃ¶bius function is strongly orthogonal to polynomial phases over Fp​[t]

Low-codimensional Subvarieties Inside Dense Multilinear Varieties

A Bilinear Bogolyubov Argument in Abelian Groups

Quasipolynomial inverse theorem for the U4(Fpn​) norm

Good bounds for sets lacking skew corners

General inverse theory for the $U^{4}$ norm

MÃ¶bius function is strongly orthogonal to polynomial phases over $F_{p} [t]$

Quasipolynomial inverse theorem for the $U^{4} (F_{p}^{n})$ norm