Problems in Algebraic Number Theory [electronic resource] / by M. Ram Murty, Jody Esmonde.

By: Murty, M. Ram [author.]
Contributor(s): Esmonde, Jody [author.] | SpringerLink (Online service)
Material type: TextTextSeries: Graduate Texts in Mathematics: 190Publisher: New York, NY : Springer New York, 2005Edition: Second EditionDescription: XVI, 352 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387269986Subject(s): Mathematics | Number theory | Mathematics | Number TheoryAdditional physical formats: Printed edition:: No titleDDC classification: 512.7 LOC classification: QA241-247.5Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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Problems in Algebraic Number Theory (Graduate Texts in Mathematics). by Murty, M. Ram. ©2010

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