03417nam a22004455i 4500 978-0-387-26998-6 DE-He213 20260521091841.0 cr nn 008mamaa 100301s2005 xxu| s |||| 0|eng d 9780387269986 99780387269986 10.1007/b138452 doi CICY 512.7 23 Murty, M. Ram. author. Problems in Algebraic Number Theory [recurso electrónico] / by M. Ram Murty, Jody Esmonde. Second Edition. New York, NY : Springer New York, 2005. XVI, 352 p. online resource. text txt rdacontent computer c rdamedia recurso en línea cr rdacarrier text file PDF rda Graduate Texts in Mathematics, 0072-5285 ; 190 Problems -- 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. 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. Metsänkylä , 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. MATHEMATICS. NUMBER THEORY. MATHEMATICS. NUMBER THEORY. Esmonde, Jody. author. SpringerLink (Online service) Springer eBooks Printed edition: 9780387221823 Graduate Texts in Mathematics, 0072-5285 ; 190 http://dx.doi.org/10.1007/b138452 Ver el texto completo en las instalaciones del CICY ddc ER 32543 32543 0 0 ddc 0 0 LE CICY CICY EL 2025-07-10 0 512.7 2025-07-10 08:39:37 2025-07-10 ER