Hamed Mousavi

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20232026

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5 papers · 1 filter

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…