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024 7 $a10.1007/978-3-319-45955-4
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035   $a(DE-He213)978-3-319-45955-4
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035   $a(MiAaPQ)EBC5592217
035   $a(Au-PeEL)EBL5592217
035   $a(OCoLC)964656014
035   $a(PPN)197133150
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100   $a20161114d2016      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aQuadratic Residues and Non-Residues$b[electronic resource] $eSelected Topics /$fby Steve Wright
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XIII, 292 p. 20 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2171
311   $a3-319-45954-6 
327   $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.
330   $aThis book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet?s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2171
606   $aNumber theory
606   $aCommutative algebra
606   $aCommutative rings
606   $aAlgebra
606   $aField theory (Physics)
606   $aConvex geometry 
606   $aDiscrete geometry
606   $aFourier analysis
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
606   $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014
606   $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058
615  0$aNumber theory.
615  0$aCommutative algebra.
615  0$aCommutative rings.
615  0$aAlgebra.
615  0$aField theory (Physics).
615  0$aConvex geometry .
615  0$aDiscrete geometry.
615  0$aFourier analysis.
615 14$aNumber Theory.
615 24$aCommutative Rings and Algebras.
615 24$aField Theory and Polynomials.
615 24$aConvex and Discrete Geometry.
615 24$aFourier Analysis.
676   $a510
700   $aWright$b Steve$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441712
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466765803316
996   $aQuadratic residues and non-residues$91412561
997   $aUNISA