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

We provide a new arithmetic characterization for the sequence of coefficients of algebraic power series $f(t)$ having the property that the differential equation $y^{\mathrm{\prime }}(t)=f(t)y(t)$ 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.