29 citations · 181 across the 37 of their papers we have counts for
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math.DS2013
Cotlar's ergodic theorem along the prime numbers
Mariusz Mirek, Bartosz Trojan
The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.
math.CA2013
Weak type (1, 1) inequalities for discrete rough maximal functions
Mariusz Mirek
The aim of this paper is to show that the discrete maximal function $$\mathcal{M}_{h}f(x)=\sup_{N\in\mathbb{N}}\frac{1}{|\mathbf{N}_{h}\cap[1, N]|}\Big|\sum_{n\in \mathbf{N}_{h}\ca…
math.CA2013
Roth's Theorem in the Piatetski-Shapiro primes
Mariusz Mirek
Let denote the set of prime numbers and, for an appropriate function , define a set $\mathbf{P}_{h}=\{p\in\mathbf{P}: \exists_{n\in\mathbb{N}}\ p=\lfloor h(n)\rfloo…