Diophantine Analysis

1st Edition

Jorn Steuding

Chapman and Hall/CRC
Published May 19, 2005
Textbook - 280 Pages - 11 B/W Illustrations
ISBN 9781584884828 - CAT# C4827
Series: Discrete Mathematics and Its Applications

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  • Provides a modern introduction to diophantine analysis, with emphasis on the interactions between the theory of diophantine approximation and the theory of diophantine equations
  • Requires only an elementary background in number theory and algebra
  • Presents new topics such as the abc-conjecture and the irrationality of the zeta function
  • Discusses topics related to discrete mathematics, including factoring large integers, error-free computing, and factoring polynomials
  • Includes problem sections at the end of every chapter
  • Summary

    While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain.

    Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers.

    Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.


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