Discriminant equations are an important class of Diophantine
equations with close ties to algebraic number theory, Diophantine
approximation and Diophantine geometry. This book is the first
comprehensive account of discriminant equations and their
applications. It brings together many aspects, including effective
results over number fields, effective results over finitely
generated domains, estimates on the number of solutions,
applications to algebraic integers of given discriminant, power
integral bases, canonical number systems, root separation of
polynomials and reduction of hyperelliptic curves. The authors'
previous title, Unit Equations in Diophantine Number Theory, laid
the groundwork by presenting important results that are used as
tools in the present book. This material is briefly summarized in
the introductory chapters along with the necessary basic algebra
and algebraic number theory, making the book accessible to experts
and young researchers alike.
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