You are here  Lecture Notes on Diophantine Analysis  Umberto
Zannier Edizioni della Normale Publication Date:  Number of
Pages:  Lecture Notes 8 [Reviewed by Felipe Zaldivar , on
Solving polynomial equations in integer or rational numbers is a
classical arithmetic problem that can be traced back to the
Babylonians but that was studied systematically by Diophantus of
Alexandria (ca. 250 AD). Determining whether a given set of
polynomial equations has solutions in integer or rational
numbers, or finding all such solutions, or counting the number
of solutions, are called Diophantine problems. Since a set of
polynomial equations defines an affine or projective variety
(e.g., over the field of complex numbers) the integer or
rational solutions are points on this variety and the language
of algebraic geometry gives an appropriate setting to formulate
and study these problems, hence the name Diophantine geometry,
which accurately describes this feature.  Zannier’s book is a
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