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Book Review
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Book Information
Author(s):
Joseph H. Silverman and John T. Tate
Title:
Rational points on elliptic curves
Additional book information:
Undergraduate Texts in Mathematics, Springer-Verlag, New York and Berlin, 1992 (first ed. 1989), x+281 pp., US$29.95. ISBN 0-387-97825-9
References:
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- J. W. S. Cassels, Lectures on elliptic curves, Cambridge Univ. Press, Cambridge and New York, 1991.
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- J.~Chahal, Topics in number theory, Plenum Press, New York and London, 1988.
- [4]
- D. A.~Cox, Primes of the form $x^2 + ny^2$\RM : Fermat, class field theory, and complex multiplication, Wiley, New York, 1989.
- [5]
- J. E.~Cremona, Algorithms for modular elliptic curves, Cambridge Univ. Press, Cambridge and New York, 1992.
- [6]
- S.~Fermigier, Un exemple de courbe elliptique d\'efinie sur~$\Q $ de rang~$\ge 19$, C. R. Acad. Sci. Paris S\'er. I Math. \textbf{315} (1992), 719--722.
- [7]
- G. Frey, Links between stable elliptic curves and certain diophantine equations, Ann. Univ. Sarav. Ser. Math. \textbf{1} (1986), 1--40.
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- A. Granville, \emph{On the Kummer-Wieferich-Skula approach to the first case of Fermat\RM 's Last Theorem}, Clarendon Press, Oxford, 1993 pp.~479--498.
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- A. Granville and M. B. Monagan, The first case of Fermat\,\RM 's last theorem is true for all prime exponents up to \rm 714,591,416,091,389, Trans. Amer. Math. Soc. \textbf{306} (1988), 329--359.
- [10]
- B. H. Gross, \emph{Kolyvagin\RM 's work on modular elliptic curves} vol.~153, Cambridge Univ. Press, Cambridge, 1991 pp.~235--256.
- [11]
- B. H. Gross and D. B. Zagier, Heegner points and the derivatives of $L$-series, Invent. Math. \textbf{84} (1986), 225--320.
- [12]
- D. Husem\"oller, Elliptic curves, Graduate Texts in Math., vol. 111, Springer-Verlag, Berlin and New York, 1987.
- [13]
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- [14]
- A. W.~Knapp, Elliptic curves, Math. Notes, vol. 40, Princeton Univ. Press, Princeton, NJ, 1992.
- [15]
- N. Koblitz, Introduction to elliptic curves and modular forms, Graduate Texts in Math., vol. 97, Springer-Verlag, Berlin and New York, 1984.
- [16]
- V. Kolyvagin, \emph{Euler systems} vol.~87, Birkh\"auser, Boston, 1990 pp.~435--483.
- [17]
- S. Lang, Elliptic curves diophantine analysis, Grundlehren der Math. Wiss., vol. 231, Springer-Verlag, Berlin and New York, 1978.
- [18]
- H. W. Lenstra, Jr., Factoring integers with elliptic curves, Ann. of Math. (2) \textbf{126} (1987), 649--673.
- [19]
- B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes \'Etudes Sci. Publ. Math. \textbf{47} (1977), 33--186.
- [20]
- B. Mazur, Number theory as gadfly, Amer. Math. Monthly \textbf{98} (1991), 593--610.
- [21]
- K. A. Ribet, On modular representations of $\GalQ $ arising from modular forms, Invent. Math. \textbf{100} (1990), 431--476.
- [22]
- K. A. Ribet, From the Taniyama-Shimura Conjecture to Fermat\RM 's Last Theorem, Ann. Fac. Sci. Toulouse Math. (5) \textbf{11} (1990), 116--139.
- [23]
- J. P. Serre, \emph{Lettre \`a J. F. Mestre} vol.~67, Amer. Math. Soc., Providence, RI, 1987 pp.~263--268.
- [24]
- J. P. Serre, Sur les repr\'esentations modulaires de degr\'e \RM 2 de $\GalQ $, Duke Math. J. \textbf{54} (1987), 179--230.
- [25]
- J. H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Math., vol. 106, Springer-Verlag, Berlin and New York, 1986.
- [26]
- J. W. Tanner and S. S. Wagstaff, Jr., New bounds for the first case of Fermat\RM 's Last Theorem, Math. Comp. \textbf{53} (1989), 743--750.
- [27]
- J. T. Tate, The arithmetic of elliptic curves, Invent. Math. \textbf{23} (1974), 179--206.
- [28]
- M. Waldschmidt et al., eds., From number theory to physics \rm (Lectures given at the meeting ``Number Theory and Physics" held at the Centre de Physique, Les Houches, 1989), Springer-Verlag, Berlin and New York, 1992.
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- A. Wiles, Modular elliptic curves and Fermat\RM 's Last Theorem.
Additional Information:
Reviewer(s):
William R.
Hearst III
Reviewer(s):
Kenneth A.
Ribet
Review Information:
Journal:
Bull. Amer. Math. Soc.
30
(1994),
248-252.
DOI:
10.1090/S0273-0979-1994-00465-3
PII:
S 0273-0979(1994)00465-3
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