LEADER 00713nam0-22002771i-450- 001 990003346680403321 005 20001010 035 $a000334668 035 $aFED01000334668 035 $a(Aleph)000334668FED01 035 $a000334668 100 $a20001010d--------km-y0itay50------ba 101 0 $aita 105 $ay-------001yy 200 1 $a<>WORLD OF VIOLENCE 210 $aLONDON$cVICTOR COLLANCZ LTD$d1963 676 $a045 700 1$aWilson,$bColin$f<1931- >$0193246 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990003346680403321 952 $a045 WIL /7$bLINGUE 1047$fDECLI 959 $aDECLI 996 $aWORLD OF VIOLENCE$9442960 997 $aUNINA DB $aING01 LEADER 05651nam 22005892 450 001 9910136612203321 005 20161103102045.0 010 $a1-316-72721-1 010 $a1-316-72841-2 010 $a1-316-72861-7 010 $a1-316-16076-9 010 $a1-316-72881-1 010 $a1-316-72961-3 010 $a1-316-72901-X 035 $a(CKB)3710000000894278 035 $a(EBL)4697936 035 $a(UkCbUP)CR9781316160763 035 $a(MiAaPQ)EBC4697936 035 $a(EXLCZ)993710000000894278 100 $a20140731d2017|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDiscriminant equations in Diophantine number theory /$fJanj-Hendrik Evertse, Ka?lma?n Gyo?ry$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2017. 215 $a1 online resource (xviii, 457 pages) $cdigital, PDF file(s) 225 1 $aNew Mathematical monographs ;$v32 300 $aTitle from publisher's bibliographic system (viewed on 01 Nov 2016). 311 $a1-107-09761-4 311 $a1-316-72941-9 320 $aIncludes bibliographical references and index. 327 $aCover; Half title; Series; Title; Copyright; Contents; Preface; Acknowledgments; Summary; Part One Preliminaries; 1 Finite E?tale Algebras over Fields; 1.1 Terminology for Rings and Algebras; 1.2 Finite Field Extensions; 1.3 Basic Facts on Finite E?tale Algebras over Fields; 1.4 Resultants and Discriminants of Polynomials; 1.5 Characteristic Polynomial, Trace, Norm, Discriminant; 1.6 Integral Elements and Orders; 2 Dedekind Domains; 2.1 Definitions; 2.2 Ideal Theory of Dedekind Domains; 2.3 Discrete Valuations; 2.4 Localization; 2.5 Integral Closure in Finite Field Extensions 327 $a2.6 Extensions of Discrete Valuations2.7 Norms of Ideals; 2.8 Discriminant and Different; 2.9 Lattices over Dedekind Domains; 2.10 Discriminants of Lattices of E?tale Algebras; 3 Algebraic Number Fields; 3.1 Definitions and Basic Results; 3.1.1 Absolute Norm of an Ideal; 3.1.2 Discriminant, Class Number, Unit Group and Regulator; 3.1.3 Explicit Estimates; 3.2 Absolute Values: Generalities; 3.3 Absolute Values and Places on Number Fields; 3.4 S-integers, S-units and S-norm; 3.5 Heights and Houses; 3.6 Estimates for Units and S-units 327 $a3.7 Effective Computations in Number Fields and E?tale Algebras3.7.1 Algebraic Number Fields; 3.7.2 Relative Extensions and Finite E?tale Algebras; 4 Tools from the Theory of Unit Equations; 4.1 Effective Results over Number Fields; 4.1.1 Equations in Units of Rings of Integers; 4.1.2 Equations with Unknowns from a Finitely Generated Multiplicative Group; 4.2 Effective Results over Finitely Generated Domains; 4.3 Ineffective Results, Bounds for the Number of Solutions; Part Two Monic Polynomials and Integral Elements of Given Discriminant, Monogenic Orders; 5 Basic Finiteness Theorems 327 $a5.1 Basic Facts on Finitely Generated Domains5.2 Discriminant Forms and Index Forms; 5.3 Monogenic Orders, Power Bases, Indices; 5.4 Finiteness Results; 5.4.1 Discriminant Equations for Monic Polynomials; 5.4.2 Discriminant Equations for Integral Elements in E?tale Algebras; 5.4.3 Discriminant Form and Index Form Equations; 5.4.4 Consequences for Monogenic Orders; 6 Effective Results over Z; 6.1 Discriminant Form and Index Form Equations; 6.2 Applications to Integers in a Number Field; 6.3 Proofs; 6.4 Algebraic Integers of Arbitrary Degree; 6.5 Proofs 327 $a6.6 Monic Polynomials of Given Discriminant6.7 Proofs; 6.8 Notes; 6.8.1 Some Related Results; 6.8.2 Generalizations over Z; 6.8.3 Other Applications; 7 Algorithmic Resolution of Discriminant Form and Index Form Equations; 7.1 Solving Discriminant Form and Index Form Equations via Unit Equations, A General Approach; 7.1.1 Quintic Number Fields; 7.1.2 Examples; 7.2 Solving Discriminant Form and Index Form Equations via Thue Equations; 7.2.1 Cubic Number Fields; 7.2.2 Quartic Number Fields; 7.2.3 Examples; 7.3 The Solvability of Index Equations in Various Special Number Fields; 7.4 Notes 327 $a8 Effective Results over the S-integers of a Number Field 330 $aDiscriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike. 410 0$aNew Mathematical monographs ;$v32. 606 $aDiophantine equations 615 0$aDiophantine equations. 676 $a512.74 700 $aEvertse$b J. H.$01075479 702 $aGyo?ry$b Ka?lma?n 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910136612203321 996 $aDiscriminant equations in Diophantine number theory$92584983 997 $aUNINA