This is an English translation of Ostrowski's article "\"Uber Dirichletsche
Reihen und algebraische Differentialgleichungen" published German in Math.
Zeit. vol. 8, 1920, pp. 241-298. In this article, Ostrowski proves a conjecture
of Hilbert that the two variable function ζ(x,s)=∑n≥1​nsxn​ cannot be written as a composition of analytic functions of
one variable and algebraic functions of any number of variables.Comment: 50 pages. Comments welcome