7 papers
Quantitative bounds for sets lacking polynomial progressions with shifted prime difference
Ben Krause, Hamed Mousavi, Terence Tao +1
We prove quantitative polynomial Szemerédi-type theorems involving polynomial progressions with shift parameter restricted to the set of shifted primes . The types of…
Pointwise Convergence of Ergodic Averages Along Integer Cantor Sets
Félix Brokering Pinilla, Alex Iosevich, Ben Krause
Let , \[ D \subsetneq \{ 0,1,\dots,d-1\}, \qquad |D| \geq 2, \ 0 \in D \] be a finite alphabet, and define the integer Cantor set \begin{align} \mathcal{C} := \mathcal{C}…
The Wiener Wintner Theorem Along the Primes
Jan Fornal, Anastasios Fragkos, Ben Krause +3
We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability sp…
Cross representations of additive complements of -th powers
Yuchen Ding, Ben Krause, Csaba Sándor +2
Let be the set of natural numbers and the set of -th powers, where is a natural number. Let $\mathcal{W}_r…
A Variation Norm Carleson Theorem Along the Primes
Anastasios Fragkos, Ben Krause, Nazar Miheisi +1
Let denote the von Mangoldt function; we prove that for each , there exist constants \[ r' < \mathbf{c}(r) < 2 < \mathbf{C}(r), \qquad \lim_{r \to \infty} \mathbf{c}(r)…
Double Recurrence and Almost Sure Convergence: Primes and Weighted Theory
Jan Fornal, Ben Krause
Let be a probability space equipped with an invertible, measure-preserving transformation . We exhibit a wide class of weights so that whenever $f,g \…