Book Review
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MathSciNet review:
1567919
Full text of review:
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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.
1. L. R. Ford, A geometrical proof of a theorem of Hurwitz, Proc. Edinburgh Math. Soc. 35 (1917), 59-65.
L. R. Ford, Fractions, Amer. Math. Monthly 45 (1938), no. 9, 586–601. MR 1524411, DOI 10.2307/2302799
G. A. Freĭman, Diofantovy priblizheniya i geometriya chisel (zadacha Markova), Kalinin. Gosudarstv. Univ., Kalinin, 1975 (Russian). MR 0485714
Marshall Hall Jr., On the sum and product of continued fractions, Ann. of Math. (2) 48 (1947), 966–993. MR 22568, DOI 10.2307/1969389
A. Hurwitz, Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche, Math. Ann. 39 (1891), no. 2, 279–284 (German). MR 1510702, DOI 10.1007/BF01206656
Gregori Aleksandrovitch Margulis, Formes quadratriques indéfinies et flots unipotents sur les espaces homogènes, C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), no. 10, 249–253 (English, with French summary). MR 882782
G. A. Margulis, Discrete subgroups and ergodic theory, Number theory, trace formulas and discrete groups (Oslo, 1987) Academic Press, Boston, MA, 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.
Alexander Oppenheim, The minima of indefinite quaternary quadratic forms, Ann. of Math. (2) 32 (1931), no. 2, 271–298. MR 1502997, DOI 10.2307/1968191
A. Oppenheim, Values of quadratic forms. I, Quart. J. Math. Oxford Ser. (2) 4 (1953), 54–59. MR 54650, DOI 10.1093/qmath/4.1.54
12. O. Perron, Über die Approximation irrationaler Zahlen durch rationale, II, S.-B. Heidelberg Akad. Wiss. Abh. 8 (1981), 12 pp.
- 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