The Resource Quadratic Residues and Non-Residues : Selected Topics, by Steve Wright, (electronic resource)

Quadratic Residues and Non-Residues : Selected Topics, by Steve Wright, (electronic resource)

Label
Quadratic Residues and Non-Residues : Selected Topics
Title
Quadratic Residues and Non-Residues
Title remainder
Selected Topics
Statement of responsibility
by Steve Wright
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Wright, Steve
Image bit depth
0
LC call number
QA241-247.5
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Lecture Notes in Mathematics,
Series volume
2171
http://library.link/vocab/subjectName
  • Mathematics
  • Commutative algebra
  • Commutative rings
  • Algebra
  • Field theory (Physics)
  • Fourier analysis
  • Convex geometry
  • Discrete geometry
  • Number theory
  • Mathematics
  • Number Theory
  • Commutative Rings and Algebras
  • Field Theory and Polynomials
  • Convex and Discrete Geometry
  • Fourier Analysis
Label
Quadratic Residues and Non-Residues : Selected Topics, by Steve Wright, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
XIII, 292 p. 20 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319459554
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-45955-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-45955-4
Label
Quadratic Residues and Non-Residues : Selected Topics, by Steve Wright, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
XIII, 292 p. 20 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319459554
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-45955-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-45955-4

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