LEADER 03151nam a2200445 i 4500 001 991003506889707536 006 m o d 007 cr cnu|||unuuu 008 180530s2016 sz 000 0 eng d 020 $a9783319459554 020 $a9783319459547 024 7 $a10.1007/978-3-319-45955-4$2doi 035 $ab14343794-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a512.7$223 084 $aAMS 11A15 084 $aLC QA241-247.5 100 1 $aWright, Steve$0441712 245 10$aQuadratic residues and non-residues$h[e-book] :$bselected topics /$cby Steve Wright 260 $aCham :$bSpringer,$c2016 300 $a1 online resource (xiii, 292 p. 20 ill.) 490 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2171 505 0 $aChapter 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 520 $aThis book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet?s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory 650 0$aCommutative algebra 650 0$aCommutative rings 650 0$aAlgebra 650 0$aField theory (Physics) 650 0$aFourier analysis 650 0$aConvex geometry 650 0$aDiscrete geometry 650 0$aNumber theory 773 0 $aSpringer eBooks 776 08$iPrinted edition:$z9783319459547 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-45955-4$zAn electronic book accessible through the World Wide Web 907 $a.b14343794$b03-03-22$c30-05-18 912 $a991003506889707536 996 $aQuadratic residues and non-residues$91412561 997 $aUNISALENTO 998 $ale013$b30-05-18$cm$d@ $e-$feng$gsz $h0$i0