Geometry of Continued Fractions

種類:

電子ブック

責任表示:

by Oleg Karpenkov

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013

著者名:

• Karpenkov, Oleg
• SpringerLink (Online service)

シリーズ名:

Algorithms and Computation in Mathematics ; 26

ISBN:

9783642393686 [3642393683]    

注記:

Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses

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