Arithmetic properties of power series solutions of algebraic differential equations

in some non-trivial disk. We considered such a problem at a regular singular point and also at an irregular singular point. The problem at a regular singular point was more difficult. To deal with this difficulty, we utilized a Newton iteration procedure. This procedure was originally used by J. Moser and V. I. Arnol'd to deal with small divisors in celestial mechanics (cf. S. Sternberg 1141). In the present work, we improve our previous results so that they imply the following Main Theorem (cf. Chapter 4): Let Q be the algebraic closure of the rational numbers. Let y