Author

Ge Zhang

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Preprint Oct 2026

A Bogomolov property for moduli spaces of polynomials over abelian extensions

Let $d\geq2$ be an integer, and let $\operatorname{MPoly}^d$ be the moduli space of degree-$d$ polynomials. For every number field $K$, we prove that there exists $\epsilon_{K,d}>0$ such that \[ \left\lbrace\alpha\in\operatorname{MPoly}^d(K^{\mathrm{ab}})\colon h_{\mathrm{crit}}(\alpha)<\epsilon_{K,d}\right\rbrace=\lef...

Ge Zhang · 0 citations

Preprint Aug 2026

$13$ unknowns over quadratic integer rings and Lucas congruences

For every quadratic number field $K$, we prove a uniform $3$-unknown Diophantine definition of integer tuples in $\mathcal{O}_K$, allowing finitely many polynomial nonvanishing conditions. This yields an effective $+3$ transfer principle and a $13$-unknown representation of every recursively enumerable integer relation...

Ge Zhang · 0 citations