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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$b[electronic resource] /$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 $aGraduate Texts in Mathematics,$x0072-5285 ;$v84
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-387-97329-X 
311   $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,$x0072-5285 ;$v84
606   $aNumber theory
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
615  0$aNumber theory.
615 14$aNumber Theory.
676   $a512.7
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
906   $aBOOK
912   $a9910480132003321
996   $aClassical introduction to modern number theory$9375761
997   $aUNINA