03252nam 22005415 450 991048013200332120200704024758.01-4757-2103-X10.1007/978-1-4757-2103-4(CKB)2660000000022208(SSID)ssj0000898785(PQKBManifestationID)11562070(PQKBTitleCode)TC0000898785(PQKBWorkID)10922510(PQKB)11469091(DE-He213)978-1-4757-2103-4(MiAaPQ)EBC3085232(PPN)238081397(EXLCZ)99266000000002220820130321d1990 u| 0engurnn|008mamaatxtccrA Classical Introduction to Modern Number Theory[electronic resource] /by Kenneth Ireland, Michael Rosen2nd ed. 1990.New York, NY :Springer New York :Imprint: Springer,1990.1 online resource (XIV, 394 p.) Graduate Texts in Mathematics,0072-5285 ;84Bibliographic Level Mode of Issuance: Monograph0-387-97329-X 1-4419-3094-9 Includes bibliographical references and index.1 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.Bridging 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.Graduate Texts in Mathematics,0072-5285 ;84Number theoryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Number theory.Number Theory.512.7Ireland Kennethauthttp://id.loc.gov/vocabulary/relators/aut57618Rosen Michaelauthttp://id.loc.gov/vocabulary/relators/autBOOK9910480132003321Classical introduction to modern number theory375761UNINA