Leonidas Daskalakis

activity

20222026

collaborators

8 papers

math.NT2026

Pointwise ergodic theorems along sequences of intermediate growth

Leonidas Daskalakis, Mariusz Mirek, Máté Wierdl

We establish the first pointwise convergence result for ergodic averages with iterates along explicit and deterministic sequences of intermediate growth, that is, growing faster th…

math.DS2025

Pointwise convergence of ergodic averages along quadratic bracket polynomials

Leonidas Daskalakis

We establish a pointwise convergence result for ergodic averages modeled along orbits of the form $(n ⌊ n k ⌋)_{n \in N}$ , where $k$ is an arbitrary positive…

math.DS2025

Ergodic theorems for bilinear averages, Roth's Theorem and Corners along fractional powers

Leonidas Daskalakis

We prove that for every $c \in (1, 23/22)$ , every probability space $(X, B, μ)$ equipped with two commuting measure-preserving transformations $T, S : X \to X$ and every $f,…

math.DS2025

Pointwise ergodic theorems for non-conventional bilinear averages along $(⌊ n^{c} ⌋, - ⌊ n^{c} ⌋)$

Leonidas Daskalakis

For every $c \in (1, 23/22)$ and every probability dynamical system $(X, B, μ, T)$ we prove that for any $f, g \in L_{μ}^{\infty} (X)$ the bilinear ergodic averages \[ \frac{1}{N}\s…

math.DS2024

Pointwise ergodic theorems along fractional powers of primes

Erik Bahnson, Leonidas Daskalakis, Abbas Dohadwala +1

We establish pointwise convergence for nonconventional ergodic averages taken along $⌊ p^{c} ⌋$ , where $p$ is a prime number and $c \in (1, 4/3)$ on $L^{r}$ , $r \in (1, \infty)$ .…

math.DS2024

Fractionally modulated discrete Carleson's Theorem and pointwise Ergodic Theorems along certain curves

Leonidas Daskalakis, Anastasios Fragkos

For $c \in (1, 2)$ we consider the following operators \[ \mathcal{C}_{c}f(x) = \sup_{λ\in [-1/2,1/2)}\bigg| \sum_{n \neq 0}f(x-n) \frac{e^{2πiλ\lfloor |n|^{c} \rfloor}}{n}\bigg|\text…

math.CA2023

Weak-type (1,1) inequality for discrete maximal functions and pointwise ergodic theorems along thin arithmetic sets

Leonidas Daskalakis

We establish weak-type $(1, 1)$ bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin deterministic sets $B$ . As a corollary we…

math.CA2022

Roth's Theorem and the Hardy--Littlewood majorant problem for thin subsets of primes

Leonidas Daskalakis

We introduce a wide class of deterministic subsets of primes of zero relative density and we prove Roth's Theorem in these sets, namely, we show that any subset of them with positi…

Pointwise ergodic theorems along sequences of intermediate growth

Pointwise convergence of ergodic averages along quadratic bracket polynomials

Ergodic theorems for bilinear averages, Roth's Theorem and Corners along fractional powers

Pointwise ergodic theorems for non-conventional bilinear averages along (⌊nc⌋,−⌊nc⌋)

Pointwise ergodic theorems along fractional powers of primes

Fractionally modulated discrete Carleson's Theorem and pointwise Ergodic Theorems along certain curves

Weak-type (1,1) inequality for discrete maximal functions and pointwise ergodic theorems along thin arithmetic sets

Roth's Theorem and the Hardy--Littlewood majorant problem for thin subsets of primes

Pointwise ergodic theorems for non-conventional bilinear averages along $(⌊ n^{c} ⌋, - ⌊ n^{c} ⌋)$