MARC record from Internet Archive

LEADER: 06252cam 2200817Ia 4500
001 ocm77795788
003 OCoLC
005 20220926075542.0
008 061213s2007 nyua b 001 0 eng d
010 $a 2007925736$z 2007925737
040 $aUKM$beng$cUKM$dBAKER$dINU$dBTCTA$dYDXCP$dWAU$dOHX$dDLC$dMUQ$dNLGGC$dNOR$dHEBIS$dUKMGB$dUMR$dOCLCF$dOCLCO$dOCLCQ$dNJR$dDHA$dOCLCQ$dVRC$dIL4J6$dOCLCO$dOKS$dOCLCO
015 $aGBA702283$2bnb
016 7 $a013639406$2Uk
019 $a1295475611
020 $a9780387499222$q(v. 1)
020 $a0387499229$q(v. 1)
020 $a9780387498935$q(v. 2)
020 $a0387498931$q(v. 2)
020 $a9780387499239$q(v. 1 ;$qe-ISBN)
020 $a0387499237$q(v. 1 ;$qe-ISBN)
020 $a9780387498942$q(v. 2 ;$qe-ISBN)
020 $a038749894X$q(v. 2 ;$qe-ISBN)
035 $a(OCoLC)77795788$z(OCoLC)1295475611
050 00 $aQA241$b.C668 2007
082 04 $a512.7$222
084 $a31.14$2bcl
100 1 $aCohen, Henri.
245 10 $aNumber theory /$cHenri Cohen.
260 $aNew York :$bSpringer,$c©2007.
300 $a2 volumes :$billustrations ;$c25 cm
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aGraduate texts in mathematics ;$v239-240
504 $aIncludes bibliographical references (v. 1. pages 615-624; v.2 p. 561-570) and indexes.
505 00 $gv. 1.$tTools and diophantine equations --$gv. 2.$tAnalytic and modern tools.
505 00 $gv. 1.$tTools and diophantine equations --$tPreface --$g1.$tIntroduction to diophantine equations --$gpt. 2.$tTools --$g3.$tBasic algebraic number theory --$g4.$t[p]-adic fields --$g5.$tQuadratic forms and local-global principles --$gpt. 2.$tDiophantine equations --$g6.$tSome diophantine equations --$g7.$tElliptic curves --$g8.$tDiophantine aspects of elliptic curves --$tBibliography --$tIndex of notation --$tIndex of names --$tGeneral index.
505 00 $gv. 2.$tAnalytic and modern tools --$tPreface --$gpt. 3.$tAnalytic tools --$g9.$tBernoulli polynomials and the gamma function --$g10.$tDirichlet series and L-functions --$g11.$t[p]-adic gamma and L-functions --$gpt. 4.$tModern tools --$g12.$tApplications of linear forms in logarithms --$g13.$tRational points on higher-genus curves --$g14.$tThe super-Fermat equation --$g15.$tThe modular approach to diophantine equations --$g16.$tCatalan's equation --$tBibliography --$tIndex of notation --$tIndex of names --$tGeneral index.
520 $a"A unique collection of topics centered on a unifying topic. Includes more than 350 exercises. Text is largely self-contained. The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results."--Publisher's website.
540 $aCurrent copyright fee: GBP19.00$c42\0.$5Uk
650 0 $aDiophantine equations.
650 0 $aNumber theory.
650 6 $aÉquations diophantiennes.
650 6 $aThéorie des nombres.
650 7 $aDiophantine equations.$2fast$0(OCoLC)fst00894090
650 7 $aNumber theory.$2fast$0(OCoLC)fst01041214
650 7 $aZahlentheorie$2gnd
650 17 $aGetaltheorie.$2gtt
650 7 $aNumber theory.$2nli
650 7 $aAlgebraic number theory.$2nli
650 7 $aDiophantine equations.$2nli
830 0 $aGraduate texts in mathematics ;$v239-240.
856 41 $uhttps://doi.org/10.1007/978-0-387-49894-2$zRutgers restricted$zFull text available from Springer
856 41 $uhttps://doi.org/10.1007/978-0-387-49923-9$zRutgers restricted$zFull text available from Springer
856 $31850-9999$uhttp://www.springer.com/gb/$xBLDSS
938 $aBaker & Taylor$bBKTY$c59.95$d59.95$i0387499229$n0007078661$sactive
938 $aBaker & Taylor$bBKTY$c59.95$d59.95$i0387498931$n0007078660$sactive
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938 $aOtto Harrassowitz$bHARR$nhar060143979
938 $aYBP Library Services$bYANK$n2492061
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948 $hNO HOLDINGS IN GTX - 333 OTHER HOLDINGS