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

2024/08/25 by Bostan, Alin
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.13951

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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