Quadratic Residues and Non-Residues: Selected Topics

di Steve Wright (Autore)

Springer International Publishing AG, 2016

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.

• Autore: Steve Wright
• Editore: Springer International Publishing AG
• Collana: Lecture Notes in Mathematics
• Anno: 2016
• Rilegatura: Paperback / softback
• Pagine: 292 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783319459547

Testo in English