000 03904nam a22005655i 4500
001 978-3-319-45955-4
003 DE-He213
005 20181204134227.0
007 cr nn 008mamaa
008 161114s2016 gw | s |||| 0|eng d
020 _a9783319459554
_9978-3-319-45955-4
024 7 _a10.1007/978-3-319-45955-4
_2doi
040 _aISI Library, Kolkata
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
100 1 _aWright, Steve.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuadratic Residues and Non-Residues
_h[electronic resource] :
_bSelected Topics /
_cby Steve Wright.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2016.
300 _aXIII, 292 p. 20 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
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 _aNumber theory.
650 0 _aAlgebra.
650 0 _aField theory (Physics).
650 0 _aDiscrete groups.
650 0 _aFourier analysis.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aCommutative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11043
650 2 4 _aField Theory and Polynomials.
_0http://scigraph.springernature.com/things/product-market-codes/M11051
650 2 4 _aConvex and Discrete Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21014
650 2 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319459547
776 0 8 _iPrinted edition:
_z9783319459561
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2171
856 4 0 _uhttps://doi.org/10.1007/978-3-319-45955-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426480
_d426480