Quadratic Residues and Non-Residues Selected Topics /

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 chapt...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Wright, Steve (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edición:1st ed. 2016.
Colección:Lecture Notes in Mathematics, 2171
Temas:
Number theory.
Commutative algebra.
Commutative rings.
Algebraic fields.
Polynomials.
Convex geometry .
Discrete geometry.
Fourier analysis.
Number Theory.
Commutative Rings and Algebras.
Field Theory and Polynomials.
Convex and Discrete Geometry.
Fourier Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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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