Author

Gal Binyamini

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Preprint Sep 2026

Ax-Schanuel for the Drinfeld $j$-function

We prove an analog of the Ax-Schanuel theorem for the Drinfeld $j$-function in odd characteristic. Roughly speaking, if the graph of $\boldsymbol{j}\colon\Omega^n\rightarrow\mathbb{A}^n_{\mathbb{C}_\infty}$ and its derivatives has an atypical intersection $\mathcal{V}$ with an algebraic variety, then $\mathcal{V}$ proj...

Gal Binyamini, Dmitry Novikov, F. Saettone · 1 citation

Preprint Sep 2026

Sharp zero estimates for trajectories of polynomial vector fields

If $f$ is a tuple of functions satisfying an algebraic ODE and $P\in{\mathbb C}(x)[f]$, it is common in applications to transcendental number theory to consider upper bounds for the order of zero of $P(x,f)$ at a given point in terms of $\operatorname{deg}_x P,\operatorname{deg}_f P$. Nesterenko introduced a condition...

Gal Binyamini, Yuval Salant · 1 citation

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