02895nmm a2200289 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001800139245010500157250001700262260004800279300003200327505055000359653001800909653001800927700003700945710003400982041001901016989003601035490003401071856006201105082001001167520142801177EB000354242EBX0100000000000000020729400000000000000.0cr|||||||||||||||||||||130626 ||| eng a97803872699861 aMurty, M. Ram00aProblems in Algebraic Number TheoryhElektronische Ressourcecby M. Ram Murty, Jody (Indigo) Esmonde a2nd ed. 2005 aNew York, NYbSpringer New Yorkc2005, 2005 aXVI, 352 pbonline resource0 aProblems -- Elementary Number Theory -- Euclidean Rings -- Algebraic Numbers and Integers -- Integral Bases -- Dedekind Domains -- The Ideal Class Group -- Quadratic Reciprocity -- The Structure of Units -- Higher Reciprocity Laws -- Analytic Methods -- Density Theorems -- Solutions -- Elementary Number Theory -- Euclidean Rings -- Algebraic Numbers and Integers -- Integral Bases -- Dedekind Domains -- The Ideal Class Group -- Quadratic Reciprocity -- The Structure of Units -- Higher Reciprocity Laws -- Analytic Methods -- Density Theorems aNumber theory aNumber Theory1 aEsmonde, Jody (Indigo)e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aGraduate Texts in Mathematics uhttps://doi.org/10.1007/b138452?nosfx=yxVerlag3Volltext0 a512.7 aFrom 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. MetsĂ¤nkylĂ¤ , Mathematical Reviews The 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, Zentralblatt This 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