A method of Mahler in transcendence theory and some of its applications
John H. Loxton · Bulletin of the Australian Mathematical Society · 1984
Remarks on transcendence theory lead to a surprising proof that the decimal expansion of an algebraic irrational is irregular and to speculations on random numbers.Kurt Mahler has introduced many profound ideas and methods into the theory of transcendental numbers.His work in this area includes detailed study of the algebraic approximations of numbers such as e, v and log 2, a new classification of real and complex numbers according to their approximation properties, and the initiation and development of p-adic transcendence theory.The particular method which I shall discuss here can be traced back to Mahler's earliest papers written in GOttingen in the 1920's.These papers were unaccountably overlooked for many years, but they have received considerable attention in recent times because of links with the theory of automata.Transcendence theory is the study of the arithmetic properties of interesting numbers.The beginnings of the subject can therefore be traced