The Mordell-Weil Theorem
作者： Kenneth Ireland , Michael Rosen
DOI: 10.1007/978-1-4757-2103-4_19
关键词: Brouwer fixed-point theorem 、 Mathematics 、 Calculus 、 Factor theorem 、 Fundamental theorem 、 Algebraic geometry 、 Diophantine geometry 、 Mordell–Weil theorem 、 Compactness theorem 、 Fundamental theorem of calculus
摘要: In this chapter we prove the celebrated theorem of Mordell—Weil for elliptic curves defined over field rational numbers. Our treatment is elementary in sense that no sophisticated results from algebraic geometry are assumed. It our desire to present a self-contained important result. The significance and implications contemporary research diophantine farreaching. following summary without proofs these developments time sketched. We hope two chapters will inspire interested student continue study by consulting more comprehensive texts on arithmetic listed bibliography chapter.
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sci-hub.se 参考文章(23)
J. S. Chahal, Topics in number theory ,(1988)
Joseph H. Silverman, The Arithmetic of Elliptic Curves ,(1986)
Serge Lang, Elliptic Curves: Diophantine Analysis ,(1978)
Neal I. Koblitz, Introduction to Elliptic Curves and Modular Forms ,(1984)
John T. Tate, Joseph H. Silverman, Rational Points on Elliptic Curves ,(1992)
Christoph J. Scriba, André Weil: Number Theory: An approach through history. From Hammurapi to Legendre. Boston/Basel/Stuttgart: Birkhäuser 1983. XXI und 375 Seiten, Ln., DM 74,-. Berichte zur Wissenschaftsgeschichte. ,vol. 10, pp. 64- 65 ,(1987) , 10.1002/BEWI.19870100116
Thomas J Kretschmer, Construction of elliptic curves with large rank Mathematics of Computation. ,vol. 46, pp. 627- 635 ,(1986) , 10.2307/2008002
J. W. S. Cassels, Diophantine Equations with Special Reference To Elliptic Curves Journal of The London Mathematical Society-second Series. pp. 193- 291 ,(1966) , 10.1112/JLMS/S1-41.1.193
J. E. Hofmann, Über zahlentheoretische Methoden Fermats und Eulers, ihre Zusammenhänge und ihre Bedeutung Archive for History of Exact Sciences. ,vol. 1, pp. 122- 159 ,(1960) , 10.1007/BF00327401
L. Carlitz, S. Chowla, The Riemann hypothesis and Hilbert's tenth problem American Mathematical Monthly. ,vol. 73, pp. 906- ,(1966) , 10.2307/2314216