Alex G. Rice

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20242026

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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.NT2024

The Furstenberg-Sárközy theorem for polynomials in one or more prime variables

John R. Doyle, Alex Rice

We establish upper bounds on the size of the largest subset of ${1, 2, \dots, N}$ lacking nonzero differences of the form $h (p_{1}, \dots, p_{ℓ})$ , where $h\in \mathbb{Z}[x_1,\dots,x…