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Viser: Quadratic Residues and Non-Residues - Selected Topics
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Quadratic Residues and Non-Residues Vital Source e-bog
Steve Wright
(2016)
Springer Nature
498,00 kr.
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Quadratic Residues and Non-Residues
Selected Topics
Steve Wright
(2016)
Sprog: Engelsk
Springer International Publishing AG
581,00 kr.
Print on demand. Leveringstid vil være ca 2-3 uger.
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Springer Nature (November 2016)
- ISBN: 9783319459554
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.
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Print: 2 sider kan printes ad gangen
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Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- 1. Udgave
- Paperback: 210 sider
- Udgiver: Springer International Publishing AG (November 2016)
- ISBN: 9783319459547
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.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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