Book Review
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MathSciNet review:
3364932
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Book Information:
Authors:
Jr. Michael J. Jacobson and
Hugh C. Williams
Title:
Solving the Pell equation
Additional book information:
CMS Books in Mathematics/Ouvrages de Math\'ematiques de la SMC,
Springer,
New York,
2009,
xx+495 pp.,
ISBN 978-0-387-84922-5,
US $59.95
J.-L. de la Grange, Solution d’un problème d’arithmétique, Mélanges de philosophie et de mathématique de la Société Royale de Turin 4 (1766–1769), 44–97 (this paper was written and submitted for publication in 1768, and it appeared in 1773; see [12, Chapter IV, §II]); Œuvres, vol. I, Gauthier-Villars, Paris, 1867, 669–731.
H.$\,$E. Dudeney, Amusements in mathematics, Thomas Nelson and Sons, London, 1917.
L. Euler, Vollständige Anleitung zur Algebra, St. Petersburg, 1770. A Russian translation had already appeared in 1768/69. Edition used: Opera omnia, series prima, volumen primum, H. Weber (ed.), B.$\,$G. Teubner, Leipzig and Berlin, 1911.
L. Euler, Elements of algebra, translated from the French [by J. Hewlett and F. Horner], two volumes, J. Johnson, London, 1797.
J.$\,$E. Hofmann, Studien zur Zahlentheorie Fermats (Über die Gleichung $x^2=py^2+1$), Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1944 (1944), no. 7, 19 pp.
H.$\,$W. Lenstra, On the calculation of regulators and class numbers of quadratic fields, J. Armitage (ed.), Journées Arithmétiques, 1980, London Math. Soc. Lecture Note Ser. 56, Cambridge University Press, Cambridge, 1982, 123–150.
D. Mumford, The lure of the abstract: tracing the parallel influences of the Zeitgeist on art and mathematics in the last 200 years, unpublished lecture.
J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1992. The English translation Algebraic number theory (1999) corrects the error, but the 2002 reprint of the German original doesn’t; one senses the influence of the GCHQ.
René Schoof, Computing Arakelov class groups, Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ., vol. 44, Cambridge Univ. Press, Cambridge, 2008, pp. 447–495. MR 2467554
Daniel Shanks, The infrastructure of a real quadratic field and its applications, Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972) Univ. Colorado, Boulder, Colo., 1972, pp. 217–224. MR 0389842
A. Weil, Number theory, an approach through history, Birkhäuser, Boston, 1984.
References
- J.-L. de la Grange, Solution d’un problème d’arithmétique, Mélanges de philosophie et de mathématique de la Société Royale de Turin 4 (1766–1769), 44–97 (this paper was written and submitted for publication in 1768, and it appeared in 1773; see [12, Chapter IV, §II]); Œuvres, vol. I, Gauthier-Villars, Paris, 1867, 669–731.
- H.$\,$E. Dudeney, Amusements in mathematics, Thomas Nelson and Sons, London, 1917.
- L. Euler, Vollständige Anleitung zur Algebra, St. Petersburg, 1770. A Russian translation had already appeared in 1768/69. Edition used: Opera omnia, series prima, volumen primum, H. Weber (ed.), B.$\,$G. Teubner, Leipzig and Berlin, 1911.
- L. Euler, Elements of algebra, translated from the French [by J. Hewlett and F. Horner], two volumes, J. Johnson, London, 1797.
- J.$\,$E. Hofmann, Studien zur Zahlentheorie Fermats (Über die Gleichung $x^2=py^2+1$), Abh. Preuss. Akad. Wiss. Math.-Nat. Kl. 1944 (1944), no. 7, 19 pp.
- H.$\,$W. Lenstra, On the calculation of regulators and class numbers of quadratic fields, J. Armitage (ed.), Journées Arithmétiques, 1980, London Math. Soc. Lecture Note Ser. 56, Cambridge University Press, Cambridge, 1982, 123–150.
- D. Mumford, The lure of the abstract: tracing the parallel influences of the Zeitgeist on art and mathematics in the last 200 years, unpublished lecture.
- J. Neukirch, Algebraische Zahlentheorie, Springer, Berlin, 1992. The English translation Algebraic number theory (1999) corrects the error, but the 2002 reprint of the German original doesn’t; one senses the influence of the GCHQ.
- René Schoof, Computing Arakelov class groups, Algorithmic number theory: lattices, number fields, curves and cryptography, Math. Sci. Res. Inst. Publ., vol. 44, Cambridge Univ. Press, Cambridge, 2008, pp. 447–495. MR 2467554 (2009k:11212)
- Daniel Shanks, The infrastructure of a real quadratic field and its applications, Proceedings of the Number Theory Conference (Univ. Colorado, Boulder, Colo., 1972) Univ. Colorado, Boulder, Colo., 1972, pp. 217–224. MR 0389842 (52 \#10672)
- A. Weil, Number theory, an approach through history, Birkhäuser, Boston, 1984.
Review Information:
Reviewer:
Hendrik Lenstra
Affiliation:
Universiteit Leiden
Email:
hwl@math.leidenuniv.nl
Reviewer:
Peter Stevenhagen
Affiliation:
Universiteit Leiden
Email:
psh@math.leidenuniv.nl
Journal:
Bull. Amer. Math. Soc.
52 (2015), 345-351
DOI:
https://doi.org/10.1090/S0273-0979-2014-01483-1
Published electronically:
December 19, 2014
Review copyright:
© Copyright 2014
American Mathematical Society
