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Quadratic Residues and Non-Residues - Selected Topics (Paperback, 1st ed. 2016)
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Quadratic Residues and Non-Residues - Selected Topics (Paperback, 1st ed. 2016)
Series: Lecture Notes in Mathematics, 2171
Expected to ship within 10 - 15 working days
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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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