LEADER 03293nam 22006135 450 001 9910975421003321 005 20250818100407.0 010 $a1-4757-2103-X 024 7 $a10.1007/978-1-4757-2103-4 035 $a(CKB)2660000000022208 035 $a(SSID)ssj0000898785 035 $a(PQKBManifestationID)11562070 035 $a(PQKBTitleCode)TC0000898785 035 $a(PQKBWorkID)10922510 035 $a(PQKB)11469091 035 $a(DE-He213)978-1-4757-2103-4 035 $a(MiAaPQ)EBC3085232 035 $a(PPN)238081397 035 $a(EXLCZ)992660000000022208 100 $a20130321d1990 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 12$aA Classical Introduction to Modern Number Theory /$fby Kenneth Ireland, Michael Rosen 205 $a2nd ed. 1990. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1990. 215 $a1 online resource (XIV, 394 p.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v84 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-387-97329-X 311 08$a1-4419-3094-9 320 $aIncludes bibliographical references and index. 327 $a1 Unique Factorization -- 2 Applications of Unique Factorization -- 3 Congruence -- 4 The Structure of U(?/n?) -- 5 Quadratic Reciprocity -- 6 Quadratic Gauss Sums -- 7 Finite Fields -- 8 Gauss and Jacobi Sums -- 9 Cubic and Biquadratic Reciprocity -- 10 Equations over Finite Fields -- 11 The Zeta Function -- 12 Algebraic Number Theory -- 13 Quadratic and Cyclotomic Fields -- 14 The Stickelberger Relation and the Eisenstein Reciprocity Law -- 15 Bernoulli Numbers -- 16 Dirichlet L-functions -- 17 Diophantine Equations -- 18 Elliptic Curves -- 19 The Mordell-Weil Theorem -- 20 New Progress in Arithmetic Geometry -- Selected Hints for the Exercises. 330 $aBridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v84 606 $aNumber theory 606 $aNumber Theory 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a512.7 676 $a512.7 686 $a12-01$2msc 686 $a10-01$2msc 700 $aIreland$b Kenneth$4aut$4http://id.loc.gov/vocabulary/relators/aut$057618 702 $aRosen$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910975421003321 996 $aClassical introduction to modern number theory$9375761 997 $aUNINA