Diophantine Equations and Power Integral Bases

Theory and Algorithms

Authors: Gaál, István

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  • Provides a complete reference on index form equations and power integral bases
  • Describes algorithms and methods to efficiently solve several different types of classical Diophantine equations
  • Includes detailed numerical examples that demonstrate how the various methods of calculating index form equations can be applied
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  • ISBN 978-3-030-23865-0
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Softcover $109.99
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About this book

This 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.

Reviews

“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)

Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-030-23865-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-23864-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $109.99
price for USA in USD
  • ISBN 978-3-030-23867-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Diophantine Equations and Power Integral Bases
Book Subtitle
Theory and Algorithms
Authors
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-23865-0
DOI
10.1007/978-3-030-23865-0
Hardcover ISBN
978-3-030-23864-3
Softcover ISBN
978-3-030-23867-4
Edition Number
2
Number of Pages
XXII, 326
Number of Illustrations
2 illustrations in colour
Topics