000727574 000__ 03617cam\a2200481Ii\4500
000727574 001__ 727574
000727574 005__ 20230306140927.0
000727574 006__ m\\\\\o\\d\\\\\\\\
000727574 007__ cr\cn\nnnunnun
000727574 008__ 150609s2015\\\\sz\a\\\\ob\\\\001\0\eng\d
000727574 020__ $$a9783319185880$$qelectronic book
000727574 020__ $$a3319185888$$qelectronic book
000727574 020__ $$z9783319185873
000727574 0247_ $$a10.1007/978-3-319-18588-0$$2doi
000727574 035__ $$aSP(OCoLC)ocn910883818
000727574 035__ $$aSP(OCoLC)910883818
000727574 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dYDXCP$$dUPM$$dAZU
000727574 049__ $$aISEA
000727574 050_4 $$aQA567.2.E44
000727574 08204 $$a516.3/52$$223
000727574 1001_ $$aSilverman, Joseph H.,$$d1955-$$eauthor.
000727574 24510 $$aRational points on elliptic curves$$h[electronic resource] /$$cJoseph H. Silverman, John Tate.
000727574 250__ $$aSecond edition.
000727574 264_1 $$aCham :$$bSpringer,$$c2015.
000727574 300__ $$a1 online resource (xxii, 332 pages) :$$billustrations.
000727574 336__ $$atext$$btxt$$2rdacontent
000727574 337__ $$acomputer$$bc$$2rdamedia
000727574 338__ $$aonline resource$$bcr$$2rdacarrier
000727574 4901_ $$aUndergraduate texts in mathematics
000727574 504__ $$aIncludes bibliographical references and index.
000727574 5050_ $$aIntroduction -- Geometry and Arithmetic -- Points of Finite Order -- The Group of Rational Points -- Cubic Curves over Finite Fields -- Integer Points on Cubic Curves -- Complex Multiplication.
000727574 506__ $$aAccess limited to authorized users.
000727574 520__ $$aThe theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of this book. Topics covered include the geometry and group structure of elliptic curves, the Nagell-Lutz theorem describing points of finite order, the Mordell-Weil theorem on the finite generation of the group of rational points, the Thue-Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
000727574 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed June 9, 2015).
000727574 650_0 $$aCurves, Elliptic.
000727574 650_0 $$aRational points (Geometry)
000727574 650_0 $$aDiophantine analysis.
000727574 7001_ $$aTate, John Torrence,$$d1925-2019$$eauthor.
000727574 830_0 $$aUndergraduate texts in mathematics.
000727574 852__ $$bebk
000727574 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-18588-0$$zOnline Access$$91397441.1
000727574 909CO $$ooai:library.usi.edu:727574$$pGLOBAL_SET
000727574 980__ $$aEBOOK
000727574 980__ $$aBIB
000727574 982__ $$aEbook
000727574 983__ $$aOnline
000727574 994__ $$a92$$bISE