Diophantine Analysis - Course Notes from a Summer School

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 Bujacic 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.

List of contents

1. Linear Forms in Logarithms (by Sanda Bujacic, Alan Filipin).- 2. Metric Diophantine Approximation - From Continued Fractions to Fractals (by Simon Kristensen).- 3. A Geometric Face of Diophantine Analysis (by Tapani Matala-aho).- 4. Historical Face of Number Theory(ists) at the turn of the 19th Century (by Nicola M.R. Oswald)

Product details

• Assisted by: Jörn Steuding (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 07.07.2018
• EAN: 9783319840208
• ISBN: 978-3-31-984020-8
• No. of pages: 232
• Dimensions: 155 mm x 13 mm x 235 mm
• Weight: 379 g
• Illustrations: XI, 232 p. 34 illus., 31 illus. in color.
• Series: Trends in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; B, Mathematics and Statistics, Number Theory, Dynamical systems, Linear Form in Logarithms, Transcendence Theory, Diophantine Approximation,