John R. Doyle

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math.NT2025

Cubic points on dynamical modular curves

John R. Doyle, Alexander Galarraga

We consider the family of dynamical modular curves associated to quadratic polynomial maps and determine precisely which of these curves have infinitely many cubic points. We use t…

math.NT2024

The Furstenberg-SÃ¡rkÃ¶zy 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…