Lectures on Transcendental Numbers

Kurt Mahler (auth.), B. Diviš, W. J. Le Veque (eds.)9780387079868, 0-387-07986-6

Table of contents :
Existence and first properties of transcendental numbers….Pages 1-28
Convergent laurent series and formal laurent series….Pages 29-44
First results on the values of analytic functions at algebraic points….Pages 45-59
Linear differental equations: The lemmas of Shidlovski….Pages 60-89
Linear differential equations: A lower bound for the rank of the values of finitely many siegel E-functions at algebraic points….Pages 90-114
Linear differential equations: Shidlovski’s theorems on the transcendency and algebraic independence of values of siegel E-functions….Pages 115-144
Applications of Shidlovski’s main theorems to special functions….Pages 145-184
Formal power series as solutions of algebraic differential equations….Pages 185-212