Diophantine Analysis: Course Notes from a Summer School

Description

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker’s method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski’s geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M.R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book. Front Matter....Pages i-xi Linear Forms in Logarithms....Pages 1-59 Metric Diophantine Approximation—From Continued Fractions to Fractals....Pages 61-127 A Geometric Face of Diophantine Analysis....Pages 129-174 Historical Face of Number Theory(ists) at the Turn of the 19th Century....Pages 175-229 Back Matter....Pages 231-232