Algebraic number theory takes the reader from unique factorisation in the integers through to the modernday number field sieve. Author jan012001 paperback on free shipping on qualified orders. For alternative viewpoints, students may also like to consult the books a brief guide to algebraic number theory, by h. Barbeau, problem books in mathematics, springer 2003. Marcuss number fields is a good intro book, but its not in latex, so it looks ugly. Also doesnt do any local padic theory, so you should pair it with gouveas excellent intro padic book and you have great first course is algebraic number theory. Swinnertondyer, trinity college, university of cambridge. In mathematics, the birch and swinnertondyer conjecture describes the set of rational solutions to equations defining an elliptic curve. A brief guide to algebraic number theory a brief guide to. A course in algebraic number theory dover books on mathematics. The book covers the two basic methods of approaching algebraic number theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to fermats last theorem, as well as a comprehensive account of class field theory. A brief guide to algebraic number theory london mathematical. The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my algebraic numbers, including much more.
Buy a brief guide to algebraic number theory a brief guide to algebraic number theory by swinnertondyer, h. Ma3a6 algebraic number theory university of warwick. There is a short pages, wellwritten and dense book on the subject. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. Number theory and algebraic geometry to peter swinnerton dyer on his 75th birthday, edited by miles reid and alexei skorobogatov, lms lecture notes 303, cambridge university press, 2004 isbn 0521545188.
A standard course in algebraic number theory discusses the proofs of the main results on integral bases, discriminants, dedekind rings, class groups, dirichlets unit theorem, etc. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. The main objects that we study in algebraic number theory are number. Algebraic theory of numbers, by pierre samuel translated from french by allan j. One of the few books with a readable account of quadratic forms. The present book has as its aim to resolve a discrepancy in the textbook literature and.
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