Hamed Mousavi

activity

20232026

collaborators

10 papers

math.NT2026

Density Bounds in Hua's Theorem for Prime Squares

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi +1

We prove a density version of Hua's theorem in the five-variable case: if $P$ is a subset of the primes with relative lower density greater than $0.82$ , then every suffici…

math.CO2026

Polynomial configurations and pointwise averages along Piatetski-Shapiro sequences

Hamed Mousavi

In this paper, we prove that for every integer $k \geq 2$ and every $c > 1$ sufficiently close to $1$ , there is $κ > 0$ such that every sufficiently large subset of ${1, \dots, N}$ of d…

math.CA2026

Polynomial Ergodic Averages Along Short Intervals

Anastasios Fragkos, Hamed Mousavi, Amelia Stokolosa

We study pointwise convergence of polynomial ergodic averages over short intervals whose left endpoints tend to infinity. For a polynomial orbit of degree $d \geq 2$ and doubly lacun…

math.NT2026

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 $P - 1$ . The types of…

math.DS2026

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…

math.CA2025

An Approach To Endpoint Problems in Oscillatory Singular Integrals

Alex Iosevich, Ben Krause, Hamed Mousavi

In this note we provide a quick proof that maximal truncations of oscillatory singular integrals are bounded from $L^{1} (R)$ to $L^{1, \infty} (R)$ . The methods we us…

math.NT2024

A Density Theorem for Higher Order Sums of Prime Numbers

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi +1

Let $P$ be a subset of the primes of lower density strictly larger than $\frac{1}{2}$ . Then, every sufficiently large even integer is a sum of four primes from the set $P$ . We establis…

math.DS2024

Pointwise convergence of bilinear polynomial averages over the primes

Ben Krause, Hamed Mousavi, Terence Tao +1

We show that on a $σ$ -finite measure preserving system $X = (X, ν, T)$ , the non-conventional ergodic averages $E_{n \in [N]} Λ (n) f (T^{n} x) g (T^{P (n)} x)$ converge pointw…

math.CA2024

Averages with the Gaussian divisor: Weighted Inequalities and the Pointwise Ergodic Theorem

Christina Giannitsi, Nazar Miheisi, Hamed Mousavi

We discuss the Pointwise Ergodic Theorem for the Gaussian divisor function $d (n)$ , that is, for a measure preserving $Z [i]$ action $T$ , the limit $$\lim_{N\rightarrow \inft…

math.NT2023

Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

Christina Giannitsi, Ben Krause, Michael Lacey +2

We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $ω \subset T$ . There is an integer $N_{ω}$ , so that every odd integer $n$ …