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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 3364932
Full text of review: PDF   This review is available free of charge.
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

References [Enhancements On Off] (What's this?)

  • 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.

  • Review Information:

    Reviewer: Hendrik Lenstra
    Affiliation: Universiteit Leiden
    Reviewer: Peter Stevenhagen
    Affiliation: Universiteit Leiden
    Journal: Bull. Amer. Math. Soc. 52 (2015), 345-351
    Published electronically: December 19, 2014
    Review copyright: © Copyright 2014 American Mathematical Society