ABSTRACT
The paper gives a survey of some results on diophantine approximation (Sections 1 and 2) and their applications (Sections 3, 4 and 5). Section 1 contains an introduction to the theory of linear forms in logarithms of algebraic numbers, and Section 2 describes some results following from the Subspace Theorem. Section 3 gives applications to the local behaviour of sequences of numbers composed of small primes and of sums of two such numbers. Section 4 deals with the transcendence of infinite sums of values of a rational function and related sums, and in Section 5 some recent applications to diophantine equations and recurrence sequences are described. The Appendix contains some elaborations of Section 4. Section 3 and the Appendix contain some new results.
