4 papers · 1 filter
On deciding transcendence of power series
Alin Bostan, Bruno Salvy, Michael F. Singer
It is well known that algebraic power series are differentially finite (D-finite): they satisfy linear differential equations with polynomial coefficients. The converse problem, wh…
An arithmetic characterization of some algebraic functions and a new proof of an algebraicity prediction by Golyshev
Alin Bostan
We provide a new arithmetic characterization for the sequence of coefficients of algebraic power series having the property that the differential equation $y'(t) = f(t) y(t)…
Differential transcendence of Bell numbers and relatives: a Galois theoretic approach
Alin Bostan, Lucia Di Vizio, Kilian Raschel
In 2003 Klazar proved that the ordinary generating function of the sequence of Bell numbers is differentially transcendental over the field of meromorphic funct…
Algebraic solutions of linear differential equations: an arithmetic approach
Alin Bostan, Xavier Caruso, Julien Roques
Given a linear differential equation with coefficients in , an important question is to know whether its full space of solutions consists of algebraic functions, or…