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 ap

chapter 1|16 pages

Introduction: basic principles

chapter 2|19 pages

Classical approximation theorems

chapter 3|16 pages

Continued fractions

chapter 4|19 pages

The irrationality of ζ(3)

chapter 5|17 pages

Quadratic irrationals

chapter 6|19 pages

The Pell equation

chapter 7|13 pages

Factoring with continued fractions

chapter 8|21 pages

Geometry of numbers

chapter 9|14 pages

Transcendental numbers

chapter 10|22 pages

The theorem of Roth

chapter 11|18 pages

The abc-conjecture

chapter 12|18 pages

p-adic numbers

chapter 13|14 pages

Hensel’s lemma and applications

chapter 14|12 pages

The local–global principle