A. Lott

collaborators

5 papers

math.NT2026

The optimal van der Corput property for squares

Steve Fan, Andrew Lott

We prove a sharp quantitative form of the van der Corput property for squares. For all sufficiently large $N$ , we construct a real trigonometric polynomial $P(θ)=a_0+\sum_{1\le n\l…

math.NT2026

The van der Corput property for sums of two squares

Steve Fan, Andrew Lott

Let $S_{N} = {1 \leq d \leq N : d = x^{2} + y^{2} for some x, y \in Z} .$ We prove a power-saving form of the van der Corput property for $S_{N}$ . As a consequence, we obtain a strong Sár…

math.NT2025

Sárközy's theorem in $F_{q} [t]$ via the van der Corput property

Steve Fan, Andrew Lott

Fix a positive prime power $q$ , and let $F_{q} [t]$ be the ring of polynomials over the finite field $F_{q}$ with $char (F_{q}) > 2$ . Suppose $A \subseteq \…

math.NT2025

Polynomial progressions in the generalized twin primes

Andrew Lott, Nagendar Reddy Ponagandla

By Maynard's theorem and the subsequent improvements by the Polymath Project, there exists a positive integer $b \leq 246$ such that there are infinitely many primes $p$ such that $…

math.NT2025

Polynomial configurations in dense subsets of the prime lattice

Andrew Lott, Ákos Magyar, Giorgis Petridis +1

We provide a multidimensional extension of previous results on the existence of polynomial progressions in dense subsets of the primes. Let $A$ be a subset of the prime lattice - t…

The optimal van der Corput property for squares

The van der Corput property for sums of two squares

Sárközy's theorem in Fq​[t] via the van der Corput property

Polynomial progressions in the generalized twin primes

Polynomial configurations in dense subsets of the prime lattice

Sárközy's theorem in $F_{q} [t]$ via the van der Corput property