Quadratic Residues and Non-Residues

Selected Topics

AvSteve Wright

Häftad, Engelska, 2016

Del 2171 i serien Lecture Notes in Mathematics

612 kr

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E-bok

797 kr

Beskrivning

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory.The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

Produktinformation

Utgivningsdatum:2016-11-15
Mått:155 x 235 x 17 mm
Vikt:470 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:292
Upplaga:16001
Förlag:Springer International Publishing AG
ISBN:9783319459547

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

After earning degrees in mathematics from Western Kentucky University and Indiana University, the author joined the faculty at Oakland University, where he is now Professor of Mathematics in the Department of Mathematics and Statistics. He currently occupies his time studying number theory.

Innehållsförteckning

Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a Prime.- Chapter 2. Basic Facts.- Chapter 3. Gauss' Theorema Aureum: the Law of Quadratic Reciprocity.- Chapter 4. Four Interesting Applications of Quadratic Reciprocity.- Chapter 5. The Zeta Function of an Algebraic Number Field and Some Applications.- Chapter 6. Elementary Proofs.- Chapter 7. Dirichlet L-functions and the Distribution of Quadratic Residues.- Chapter 8. Dirichlet's Class-Number Formula.- Chapter 9. Quadratic Residues and Non-residues in Arithmetic Progression.- Chapter 10. Are quadratic residues randomly distributed?.- Bibliography.

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Quadratic Residues and Non-Residues

Selected Topics

AvSteve Wright

Häftad, Engelska, 2016

Del 2171 i serien Lecture Notes in Mathematics

612 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

E-bok

797 kr

Beskrivning

Produktinformation

Utgivningsdatum:2016-11-15
Mått:155 x 235 x 17 mm
Vikt:470 g
Format:Häftad
Språk:Engelska
Serie:Lecture Notes in Mathematics
Antal sidor:292
Upplaga:16001
Förlag:Springer International Publishing AG
ISBN:9783319459547

Utforska kategorier

Talteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

Innehållsförteckning

Chapter 1. Introduction: Solving the General Quadratic Congruence Modulo a Prime.- Chapter 2. Basic Facts.- Chapter 3. Gauss' Theorema Aureum: the Law of Quadratic Reciprocity.- Chapter 4. Four Interesting Applications of Quadratic Reciprocity.- Chapter 5. The Zeta Function of an Algebraic Number Field and Some Applications.- Chapter 6. Elementary Proofs.- Chapter 7. Dirichlet L-functions and the Distribution of Quadratic Residues.- Chapter 8. Dirichlet's Class-Number Formula.- Chapter 9. Quadratic Residues and Non-residues in Arithmetic Progression.- Chapter 10. Are quadratic residues randomly distributed?.- Bibliography.