Andrew Lott

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20212026

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math.NT2026

The Furstenberg-Sárközy theorem for sums of an even number of odd powers

Alexandros Kalogirou, Andrew Lott, Ákos Magyar +1

We obtain a Furstenberg-Sárközy-type result for sets $A \subset [N]$ whose difference set $A - A$ does not contain the sum of $s$ -many $k$ -th powers of positive integers, with $k > 1$ o…

math.NT2026

Quasipolynomial density bounds for $K$ -point configurations in $Z^{d}$

Andrew Lott, Ákos Magyar, Nagendar Reddy Ponagandla

Let $d, K, N \in N$ with $K \geq 3$ and $d \geq 4 K + 4$ . Let $Δ \subset Z^{d}$ be the vertex set of a nondegenerate $(K - 1)$ -simplex, and let $A \subseteq [N]^{d}$ contain no no…

math.NT2026

Extensions of the Furstenberg-Sárközy theorem via the arithmetic level- $d$ inequality

Carlo Francisco E. Adajar, Rishika Agrawal, Mukul Rai Choudhuri +6

Green and Sawhney recently obtained a quasipolynomial bound in the Furstenberg--Sárközy theorem for square differences by proving an ``arithmetic level-d'' inequality, thereby yiel…

math.NT2025

Notes and computations on forbidden differences

Christian Dean, Haley Havard, Elizabeth Hawkins +3

We explore from several perspectives the following question: given $X \subseteq Z$ and $N \in N$ , what is the maximum size $D (X, N)$ of $A \subseteq {1, 2, \dots, N}$ …

math.NT2022

Computations and observations on congruence covering systems

Raj Agrawal, Prarthana Bhatia, Kratik Gupta +4

A $covering system$ is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called $\texti…

The Furstenberg-Sárközy theorem for sums of an even number of odd powers

Quasipolynomial density bounds for K-point configurations in Zd

Extensions of the Furstenberg-Sárközy theorem via the arithmetic level-d inequality

Notes and computations on forbidden differences

Computations and observations on congruence covering systems

Quasipolynomial density bounds for $K$ -point configurations in $Z^{d}$

Extensions of the Furstenberg-Sárközy theorem via the arithmetic level- $d$ inequality