L. Mili'cevi'c

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20212026

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9 papers · 1 filter

math.CO2026

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

Luka Milićević

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

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

Luka Milićević, Žarko Ranđelović

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

math.CO2025

Low-codimensional Subvarieties Inside Dense Multilinear Varieties

Luka Milićević

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

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

Luka Milićević

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 Milićević

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…

math.CO2023

A collection of open problems in celebration of Imre Leader's 60th birthday

Rahil Baber, Natalie Behague, Asier Calbet +10

One of the great pleasures of working with Imre Leader is to experience his infectious delight on encountering a compelling combinatorial problem. This collection of open problems…

math.CO2023

Approximate quadratic varieties

Luka Milićević

A classical result in additive combinatorics, which is a combination of Balog-Szemerédi-Gowers theorem and a variant of Freiman's theorem due to Ruzsa, says that if a subset $A$ of…

math.CO2021

Approximately Symmetric Forms Far From Being Exactly Symmetric

Luka Milićević

Let $V$ be a finite-dimensional vector space over $F_{p}$ . We say that a multilinear form $α : V^{k} \to F_{p}$ in $k$ variables is $d$ -approximately symmetric if t…

math.CO2021

A Bilinear Bogolyubov Argument in Abelian Groups

L. Milićević

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…

General inverse theory for the U4 norm

Möbius function is strongly orthogonal to polynomial phases over Fp​[t]

Low-codimensional Subvarieties Inside Dense Multilinear Varieties

Quasipolynomial inverse theorem for the U4(Fpn​) norm

Good bounds for sets lacking skew corners

A collection of open problems in celebration of Imre Leader's 60th birthday

Approximate quadratic varieties

Approximately Symmetric Forms Far From Being Exactly Symmetric

A Bilinear Bogolyubov Argument in Abelian Groups

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

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

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