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OverviewThis monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations. In order to more efficiently determine generators of power integral bases, several algorithms and methods are presented to readers, many of which are new developments in the field. Additionally, readers are presented with various types of number fields to better facilitate their understanding of how index form equations can be solved. By introducing methods like Baker-type estimates, reduction methods, and enumeration algorithms, the material can be applied to a wide variety of Diophantine equations. This new edition provides new results, more topics, and an expanded perspective on algebraic number theory and Diophantine Analysis. Notations, definitions, and tools are presented before moving on to applications to Thue equations and norm form equations. The structure of index forms is explained, which allows readers to approach several types of number fields with ease. Detailed numerical examples, particularly the tables of data calculated by the presented methods at the end of the book, will help readers see how the material can be applied. Diophantine Equations and Power Integral Bases will be ideal for graduate students and researchers interested in the area. A basic understanding of number fields and algebraic methods to solve Diophantine equations is required. Full Product DetailsAuthor: István GaálPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 2nd ed. 2019 Weight: 0.688kg ISBN: 9783030238643ISBN 10: 3030238644 Pages: 326 Publication Date: 19 September 2019 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsReviews“The book is recommended to PhD students and researchers in the field of Diophantine equations. It can be used as a textbook for a specialized graduate course in Thue and index-form equations and as an additional reading for a general course in Diophantine equations.” (Andrej Dujella, zbMATH 1465.11090, 2021) The book is recommended to PhD students and researchers in the field of Diophantine equations. It can be used as a textbook for a specialized graduate course in Thue and index-form equations and as an additional reading for a general course in Diophantine equations. (Andrej Dujella, zbMATH 1465.11090, 2021) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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