A very extensive and geometric approach to algebraic number theory. The drawback is that the local and adelic theories are nowhere to be found in this book. Sign up or log in Sign up using Google. Clark Jul 7 '10 at
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Introduction to Cryptography Johannes Buchmann. Surreal Numbers Donald E.
Abstract Class Field Theory. We're featuring millions of their reader ratings on our book pages to help you find your new favourite book. The Global Reciprocity Law. If you want to have a pretty solid foundation of this subject, then you are suggested to read the book Lectures on Algebraic Number Theory by Neuirch which is extremely excellent in the discussion of topics even important nowadays, or the report hheory number theory by Hilbert whose foundation is indeed solid.
Extensive, but perhaps not great for beginners.
Algebraic Number Theory : Jürgen Neukirch :
Geometry of Algebraic Curves Enrico Arbarello. Algebraic Geometry Robin Hartshorne. Local Fields Jean-Pierre Serre. I love them both now, but I found Janusz understandable at a point when Neukirch was still completely impenetrable. DMV "The present work is written in a very careful and masterly fashion.
A good introduction to the subject. Also doesn't do any local p-adic theory, so you should pair it with Gouvea's excellent intro p-adic book and you have great first course is algebraic number theory.
In particular, in view of the focus of your studies, I suggest the following additional book; where additional algebrsic meant that I would not suggest it as the only book see below for explanation.
Algebraic Number Theory
I would recommend you take a look at William Stein's free online algebraic number theory textbook. It even contains what is essentially the 1-dimensional case of Arakelov Theory.
Sequential Experiments with Primes Mihai Caragiu.
Global Class Field Theory. And yes, you are not the only people thinking that it deserves to be retyped! Essays on the Theory of Numbers Richard Dedekind. Clark Jul 7 '10 at I find it neukrch be one of the most clear math books on an advanced topic, ever.
Bestsellers in Number Theory.
Algebraic Number Theory
Serge Lang's Algebraic Number Theory has a lot of general theoretical material. Pierre Samuel's "Algebraic Theory of Numbers" gives a very elegant introduction to algebraic number theory. The treatment of class field theory is The author discusses the classical concepts from the viewpoint of Arakelov theory It does not use cohomology.
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Space-Filling Curves Hans Sagan. Very hands-on, many exercises, and clear explanations. Perhaps it's a better resource for class field theory.
Cohn's book is well worth reading carefully, and Ireland and Rosen is an excellent text too. Introduction to Smooth Manifolds John M.