LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512.7
Title	Quadratic Residues and Non-Residues ([EBook]) : Selected Topics / / by Steve Wright.
Author	Wright, Steve
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XIII, 292 p. 20 illus. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 2171
ISBN	9783319459554
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-45955-4
Links to Related Works	Subject References: Algebra . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Convex and Discrete Geometry . Convex geometry . Discrete geometry . Field Theory and Polynomials . Field theory (Physics) . Fourier Analysis . Mathematics . Number Theory . Authors: Wright, Steve . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 512.7 .

Catalogue Display

Quadratic Residues and Non-Residues: Selected Topics /

Reviews