Distribution Theory of Algebraic Numbers (De Gruyter Expositions in Mathematics, 45)

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. The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair , Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann , Columbia University, New York, USA Markus J. Pflaum , University of Colorado, Boulder, USA Dierk Schleicher , Aix-Marseille Université, France Katrin Wendland , Trinity College Dublin, Dublin, Ireland Honorary Editor Victor P. Maslov , Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021) 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. Field Extensions -- Algebraic Numbers -- Algebraic Geometry -- Height Functions -- Abc-conjecture -- Roth's Theorem -- Subspace Theorems -- Vojta's Conjectures -- L-functions. By Pei-chu Hu And Chung-chun Yang. Includes Bibliographical References (p. [495]-510) And Index.

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.

"The book surveys new research 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. It is of interest to graduate students and researchers working in the area of pure mathematics."--Jacket Biographical note: Pei-Chu Hu, Shandong University, Jinan, China; Chung-Chun Yang, Hong Kong University of Science and Technology, China