An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev

Alin Bostan

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arXiv · 2408.13951

An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev

Alin Bostan

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Abstract

We provide a new arithmetic characterization for the sequence of coefficients of algebraic power series $f(t)$ having the property that the differential equation $y'(t) = f(t) y(t)$ has algebraic solutions only. This extends a recent result by Delaygue and Rivoal, and also provides a new and shorter proof of an algebraicity result predicted by Golyshev.

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Alin Bostan. 2024-08-25. An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev. https://arxiv.org/abs/2408.13951

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