Unit Equations in Diophantine Number Theory

Diophantine number theory is an active area that has seen tremendous growth over the past century and in this theory br>Unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects including effective results on br>Unit equations over number fields estimates on the number of solutions analogues for function fields and effective results for br>Unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory as well as an account of the required tools from diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.