Maximilian O'Keeffe

collaborators

3 papers

math.NT2024

SÃ¡rkÃ¶zy's Theorem for Fractional Monomials

Maximilian O'Keeffe

Suppose $A$ is a subset of ${1, \dots, N}$ which does not contain any configurations of the form $x, x + ⌊ n^{c} ⌋$ where $n \neq = 0$ and $1 < c < \frac{6}{5}$ . We show that t…

math.DS2024

Pointwise Convergence of Ergodic Averages Along Hardy Field Sequences

Maximilian O'Keeffe

Let $(X, I^¼)$ be an arbitrary measure space equipped with a family of pairwise commuting measure preserving transformations $T_{1}, \dots, T_{m}$ . We prove that the ergodic averages \[…

math.DS2024

Variational Estimates for Bilinear Ergodic Averages Along Sublinear Sequences

Maximilian O'Keeffe

We prove long variational estimates for the bilinear ergodic averages \[ A_{N;X}(f,g)(x) = \frac{1}{N} \sum_{n=1}^N f(T^{\lfloor \sqrt{n} \rfloor}x) g(T^nx) \] on an arbitrary meas…