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Book Review
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Book Information
Author(s):
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:
- 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.
Additional Information:
Reviewer(s):
Jeffrey D.
Vaaler
Review Information:
Journal:
Bull. Amer. Math. Soc.
24
(1991),
419-424.
DOI:
10.1090/S0273-0979-1991-16055-6
PII:
S 0273-0979(1991)16055-6
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