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arXiv · 1402.2346

Integral points of bounded degree on affine curves

Aaron Levin
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Abstract

We generalize Siegel's theorem on integral points on affine curves to integral points of bounded degree, giving a complete characterization of affine curves with infinitely many integral points of degree d or less over some number field. Generalizing Picard's theorem, we prove an analogous result characterizing complex affine curves admitting a nonconstant holomorphic map from a degree d (or less) analytic cover of $\mathbb{C}$.

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Aaron Levin. 2014-02-11. Integral points of bounded degree on affine curves. https://doi.org/10.1112/s0010437x15007708

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