Distribution Theory of Algebraic Numbers

The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references.

From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.

"A remarkable feature of this book is that it starts at a basic level, introducing the fundamental concepts from scratch, without proofs for the classical ones but with relevant references to more basic books for complete proofs. The authors reach gradually the most advanced recent results on qualitative and quantitative relations of algebraic numbers distributed in spaces." Zentralblatt für Mathematik