There is now much interplay between studies on logarithmic forms
and deep aspects of arithmetic algebraic geometry. New light has
been shed, for instance, on the famous conjectures of Tate and
Shafarevich relating to abelian varieties and the associated
celebrated discoveries of Faltings establishing the Mordell
conjecture. This book gives an account of the theory of linear
forms in the logarithms of algebraic numbers with special emphasis
on the important developments of the past twenty-five years. The
first part covers basic material in transcendental number theory
but with a modern perspective. The remainder assumes some
background in Lie algebras and group varieties, and covers, in some
instances for the first time in book form, several advanced topics.
The final chapter summarises other aspects of Diophantine geometry
including hypergeometric theory and the Andre-Oort conjecture. A
comprehensive bibliography rounds off this definitive survey of
effective methods in Diophantine geometry.
General
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