Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

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


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Thomas W. Cusick and Mary E. Flahive
Title: The Markoff and Lagrange spectra
Additional book information: Math. Surveys and Monographs, no. 30, Amer. Math. Soc., Providence, RI, 1989, ix + 97 pp., $42.00. ISBN 0-8218-1531-8.

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

  • 1. L. R. Ford, A geometrical proof of a theorem of Hurwitz, Proc. Edinburgh Math. Soc. 35 (1917), 59-65.
  • 2. L. R. Ford, Fractions, Amer. Math. Monthly 45 (1938), 586-601. MR 1524411
  • 3. G. A. Freiman, Diophantine approximation and geometry of numbers, (The Markoff spectrum), Kalininskii Gosudarstvennyi Universitet, Moscow, 1975. MR 485714
  • 4. M. Hall, Jr., On the sum and product of continued fractions, Ann. of Math. (2) 48 (1947), 966-993. MR 22568
  • 5. A. Hurwitz, Über die augenäherte Darstellung der Irrationalzahlen durch rationale Brüche, Math. Ann. 39 (1891), 279-284. MR 1510702
  • 6. G. A. Margulis, Formes quadratiques indéfinies et flots unipotents sur les espaces homogènes, C. R. Acad. Sci. Paris Ser. I 304 (1987), 249-253. MR 882782
  • 7. G. A. Margulis, Discrete subgroups and ergodic theory, Number Theory, Trace Formulas and Discrete Groups (K. E. Aubert, E. Bombieri, and D. Goldfeld, eds.), Academic Press, New York, 1989, pp. 377-398. MR 993328
  • 8. A. Markoff, Sur les formes quadratiques binaires indéfinies, Math. Ann. 15 (1879), 381-406.
  • 9. A. Oppenheim, The minima of indefinite quaternary quadratic forms of signature zero, Proc. Nat. Acad. Sci. USA 15 (1929), 724-727.
  • 10. A. Oppenheim, The minima of indefinite quaternary quadratic forms, Ann. of Math. (2) 32 (1931), 271-298. MR 1502997
  • 11. A. Oppenheim, Values of quadratic forms, I, Quart. J. Math. (2) 4 (1953), 54-59. MR 54650
  • 12. O. Perron, Über die Approximation irrationaler Zahlen durch rationale, II, S.-B. Heidelberg Akad. Wiss. Abh. 8 (1981), 12 pp.

Review Information:

Reviewer: Jeffrey D. Vaaler
Journal: Bull. Amer. Math. Soc. 24 (1991), 419-424
DOI: https://doi.org/10.1090/S0273-0979-1991-16055-6
American Mathematical Society