Diophantine number theory is an active area that has seen
tremendous growth over the past century, and in this theory 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 unit equations over number
fields, estimates on the number of solutions, analogues for
function fields and effective results for 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.
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