Reviews - What do customers think about Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories (Encyclopaedia of Mathematical Sciences)?
Wonderful Arithmetic Geometry Book Aug 20, 2006
This Book is a cornerstone in Arithmetic Geometry.
It is the first time in a single Book so different arguments find a common place.
Let me say that the idea of dividing the work into three parts,depending on the approach, is entirely new. In fact,
Part 1 starts with elementary theory & applications(primes,diophantine equations& approx)
Part 2 gives an account of recent ideas and theory (ch.3:Logic & Recursion, with a sketch of proof of Matiyasevic's Theorem;ch.4:Algebraic NumberTheory; ch.5:Arithmetic of Algebraic Varieties;ch.6: deals with Zeta functions and modular forms;ch.7:gives a picture, complete indeed, of Wiles'proof of Fermat Last Theorem)
Part 3 gives "Analogies and Visions",i.e. the link between numbers fields and function fields(usually this analogy is only admitted, but never explained in other books) and other analogies involving many recent arguments in Arithmetic Geometry (such as : Schottky uniformization, Arakelov Geometry, Zetas, Dynamics and Cohomology).