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Quadratic number fields

Lemmermeyer, Franz.

Quadratic number fields

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quadratic number fieldsby Franz Lemmermeyer.
作者:	Lemmermeyer, Franz.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xi, 343 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Quadratic fields.
電子資源:	https://doi.org/10.1007/978-3-030-78652-6
ISBN:	9783030786526$q(electronic bk.)

Quadratic number fields
Lemmermeyer, Franz.

Quadratic number fields[electronic resource] /by Franz Lemmermeyer. - Cham :Springer International Publishing :2021. - xi, 343 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

1. Prehistory -- 2 Quadratic Number Fields -- 3 The Modularity Theorem -- 4 Divisibility in Integral Domains -- 5 Arithmetic in some Quadratic Number Fields -- 6 Ideals in Quadratic Number Fields -- 7 The Pell Equation -- 8 Catalan's Equation -- 9 Ambiguous Ideal Classes and Quadratic Reciprocity -- 10 Quadratic Gauss Sums -- A Computing with Pari and Sage -- B Solutions -- Bibliography -- Name Index -- Subject Index.

This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.

ISBN: 9783030786526$q(electronic bk.)

Standard No.: 10.1007/978-3-030-78652-6doiSubjects--Topical Terms:

794120
Quadratic fields.

LC Class. No.: QA247 / .L3613 2021

Dewey Class. No.: 512.74

Quadratic number fields
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505 0 $a 1. Prehistory -- 2 Quadratic Number Fields -- 3 The Modularity Theorem -- 4 Divisibility in Integral Domains -- 5 Arithmetic in some Quadratic Number Fields -- 6 Ideals in Quadratic Number Fields -- 7 The Pell Equation -- 8 Catalan's Equation -- 9 Ambiguous Ideal Classes and Quadratic Reciprocity -- 10 Quadratic Gauss Sums -- A Computing with Pari and Sage -- B Solutions -- Bibliography -- Name Index -- Subject Index.
520 $a This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study. Assuming a moderate background in elementary number theory and abstract algebra, Quadratic Number Fields offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.
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