Author

Hamed Mousavi

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Preprint Aug 2026

Quantitative bounds for sets lacking polynomial progressions with shifted prime difference

We prove quantitative polynomial Szemer\'edi-type theorems involving polynomial progressions with shift parameter restricted to the set of shifted primes $\mathbb{P}-1$. The types of configurations covered are distinct degree progressions and progressions involving integer multiples of a fixed polynomial. For nonlinear...

Ben Krause, Hamed Mousavi, Terence Tao et al. · 2 citations · ⚡2

Preprint Sep 2026

Polynomial configurations and pointwise averages along Piatetski-Shapiro sequences

In this paper, we prove that for every integer $k\geq2$ and every $c>1$ sufficiently close to $1$, there is $\kappa>0$ such that every sufficiently large subset of $\{1,\ldots,N\}$ of density at least $(\log\log N)^{-\kappa}$ contains \[ x,\quad x+\lfloor n^c\rfloor,\quad x+\lfloor n^c\rfloor^2, \quad\ldots,\quad x+\lf...

Hamed Mousavi · 0 citations