Author

Dmitry Novikov

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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

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