Author

D. Zakharov

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Preprint Sep 2026

Estimating the number of real zeros of linear combinations of radicals of polynomials

We obtain upper bounds for the number of real zeros of functions of the form $$ f(x) = \sum_{k=1}^{n} c_k \bigl(P_k(x)\bigr)^{\alpha_k}, $$ where $c_k, \alpha_k \in \mathbb{R}$ and each $P_k$ is a real polynomial of degree at most $d$ that is non-negative on an interval $I\subset \mathbb{R}$. We improve previously know...

Gal Binyamini, Avner Kiro, A. Logunov et al. · 0 citations

Preprint Jul 2026

Asymptotically sharp bounds for affine subspace statistics in $\mathbb F_2^n$

Given a subset $A \subseteq \mathbb F_2^n$, we can consider the distribution of the intersection size of $A$ with a uniformly random $d$-flat $F$. Motivated by the edge statistics problem and the hypercube statistics problem, the affine subspace statistics problem concerns the maximum of $\mathbb{P}[|F\cap A|=s]$ among...

Ting-Wei Chao, Zixuan Xu, D. Zakharov · 0 citations