Andrew Lott

activity

20212026

collaborators

10 papers

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.CO2026

Refined upper bounds on Schur-like numbers

Swaroop Hegde, Andrew Lott, Giorgis Petridis +1

For positive integers $r, m$ and $N$ , every $r$ -coloring of ${1, \dots, N}$ contains a monochromatic solution to $x_{1} + \dots + x_{m + 1} = y_{1} + \dots + y_{m}$ provided that $N \ge 3^r (r!)^{…

math.DS2026

Bourgain's $L^{2}$ pointwise ergodic theorem over function fields

Thái Hoàng Lê, Andrew Lott

We prove a function-field analogue of Bourgain's $L^{2}$ pointwise ergodic theorem. Let $q$ be a power of a prime $p$ , let $F_{q} [t]$ be the ring of polynomials over the finit…

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.CO2023

The sum-product problem for small sets

Ginny Ray Clevenger, Haley Havard, Patch Heard +3

For $A \subseteq R$ , let $A + A = {a + b : a, b \in A}$ and $AA = {ab : a, b \in A}$ . For $k \in N$ , let $S P (k)$ denote the minimum value of $max {∣ A + A ∣, ∣ AA ∣}$ over all $A…

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…

math.CO2021

Schur's theorem in integer lattices

Vishal Balaji, Andrew Lott, Alex Rice

A standard proof of Schur's Theorem yields that any $r$ -coloring of ${1, 2, \dots, R_{r} - 1}$ yields a monochromatic solution to $x + y = z$ , where $R_{r}$ is the classical $r$ -color Ramsey…

math.CO2021

The pigenhole principle and multicolor Ramsey numbers

Vishal Balaji, Powers Lamb, Andrew Lott +4

For integers $k, r \geq 2$ , the diagonal Ramsey number $R_{r} (k)$ is the minimum $N \in N$ such that every $r$ -coloring of the edges of a complete graph on $N$ vertices yields o…

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

Quasipolynomial density bounds for K-point configurations in Zd

Refined upper bounds on Schur-like numbers

Bourgain's L2 pointwise ergodic theorem over function fields

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

Notes and computations on forbidden differences

The sum-product problem for small sets

Computations and observations on congruence covering systems

Schur's theorem in integer lattices

The pigenhole principle and multicolor Ramsey numbers

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

Bourgain's $L^{2}$ pointwise ergodic theorem over function fields

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