Titel: Problems in Algebraic Number Theory (Graduate Texts in Mathematics, 190)
Verlag: Springer
Erscheinungsjahr: 2010
Sprache: Englisch
ISBN-10: 1441919678
ISBN-13: 9781441919670
Einband: Softcover
Auflage: 2. Auflage
Zustand: New

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This book is a collection of about 500 problems in algebraic number theory. They are systematically arranged to reveal the evolution of concepts and ideas of the subject. All of the problems are completely solved. Any student with the usual background of undergraduate algebra should be able to work through these problems on his/her own. For this new edition the authors added a new chapter and revised several sections.

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From Reviews of the First Edition:This book provides a problem-oriented first course in algebraic number theory. ... The authors have done a fine job in collecting and arranging the problems. Working through them, with or without help from a teacher, will surely be a most efficient way of learning the theory. Many of the problems are fairly standard, but there are also problems of a more original type. This makes the book a useful supplementary text for anyone studying or teaching the subject. ... This book deserves many readers and users.- T. Mets�nkyl� , Mathematical ReviewsThe book covers topics ranging from elementary number theory (such as the unique factorization of integers or Fermat's little theorem) to Dirichlet's theorem about primes in arithmetic progressions and his class number formula for quadratic fields, and it treats standard material such as Dedekind domains, integral bases, the decomposition of primes not dividing the index, the class group, the Minkowski bound and Dirichlet's unit theorem ... the reviewer is certain that many students will benefit from this pathway into the fascinating realm of algebraic number theory.- Franz Lemmermeyer, ZentralblattThis second edition is an expanded and revised version of the first edition. In particular, it contains an extra chapter on density theorems and $L$-functions highlighting some of the analytic aspects of algebraic number theory.

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