Book Review
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MathSciNet review:
1566784
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Book Information:
Authors:
L. Kuipers and
H. Niederreiter
Title:
Uniform distribution of sequences
Additional book information:
Wiley, New York, 1974, xiv+390 pp., $24.50.
Johann Cigler and Gilbert Helmberg, Neuere Entwicklungen der Theorie der Gleichverteilung, Jber. Deutsch. Math.-Verein. 64 (1961), no. Abt. 1, 1–50 (1961) (German). MR 125102
2. J. Franel, Les suites de Farey et les problèmes des nombres premiers, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1924, 198-201.
3. G. H. Hardy and J. L. Littlewood, Some problems on diophantine approximation, Proc. Fifth Internat. Conf. Math. (Cambridge, 1912), pp. 223-229; G. H. Hardy, Collected papers. Vol. 1, Oxford Univ. Press, Oxford, 1966, pp. 20-27. MR 34 #1151.
4. G. H. Hardy and J. L. Littlewood, Some problems on diophantine approximation: The lattice points of a right-angled triangle. I, Proc. London Math. Soc. (2) 20 (1922), 15-36; G. H. Hardy, Collected papers. Vol. 1, Oxford Univ. Press, Oxford, 1966, pp. 136-158. MR 34 #1151.
M. N. Huxley, The distribution of Farey points. I, Acta Arith. 18 (1971), 281–287. MR 297722, DOI 10.4064/aa-18-1-281-287
J. F. Koksma, Diophantische Approximationen, Springer-Verlag, Berlin-New York, 1974 (German). Reprint. MR 0344200
J. F. Koksma, The theory of asymptotic distribution modulo one, Compositio Math. 16 (1964), 1–22 (1964). MR 173664
8. M. Lerch, Question 1547, Intermédiaire Math. 11 (1904), 144-145.
Wolfgang M. Schmidt, Irregularities of distribution. VII, Acta Arith. 21 (1972), 45–50. MR 319933, DOI 10.4064/aa-21-1-45-50
D. C. Spencer, The lattice points of tetrahedra, J. Math. Phys. Mass. Inst. Tech. 21 (1942), 189–197. MR 7767, DOI 10.1002/sapm1942211189
11. H. Weyl, Ueber ein Problem aus dem Gebiete der diophantischen Approximationen, Nachr. Ges. Wiss. Göttingen. Math.-Phys. Kl. 1914, 234-244; Gesammelte Abhandlungen. Band I, Springer-Verlag, Berlin and New York, 1968, pp. 487-497. MR 37 #6157.
12. H. Weyl, Sur une application de la théorie des nombres à la mécanique statistique et la théorie des perturbations, Enseignement Math. 16 (1914), 455-467. Gesammelte Abhandlungen, Band I, Springer-Verlag, Berlin and New York, 1968, pp. 498-510. MR 37 #6157.
Hermann Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), no. 3, 313–352 (German). MR 1511862, DOI 10.1007/BF01475864
S. K. Zaremba (ed.), Applications of number theory to numerical analysis, Academic Press, New York-London, 1972. MR 0334452
- 1.
- J. Cigler and G. Helmberg, Neuere Entwicklungen der Theorie der Gleichverteilung, Jber. Deutsch. Math. Verein. 64 (1961). Abt. 1, 1-50. MR 23 #A2409. MR 0125102
- 2.
- J. Franel, Les suites de Farey et les problèmes des nombres premiers, Nachr. Ges. Wiss. Göttingen Math.-Phys. Kl. 1924, 198-201.
- 3.
- G. H. Hardy and J. L. Littlewood, Some problems on diophantine approximation, Proc. Fifth Internat. Conf. Math. (Cambridge, 1912), pp. 223-229; G. H. Hardy, Collected papers. Vol. 1, Oxford Univ. Press, Oxford, 1966, pp. 20-27. MR 34 #1151.
- 4.
- G. H. Hardy and J. L. Littlewood, Some problems on diophantine approximation: The lattice points of a right-angled triangle. I, Proc. London Math. Soc. (2) 20 (1922), 15-36; G. H. Hardy, Collected papers. Vol. 1, Oxford Univ. Press, Oxford, 1966, pp. 136-158. MR 34 #1151.
- 5.
- M. N. Huxley, The distribution of Farey points. I, Acta Arith. 18 (1971), 281-287. MR 45 #6774. MR 297722
- 6.
- J. F. Koksma, Diophantische Approximationen, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 4, Springer-Verlag, Berlin, 1936. MR 344200
- 7.
- J. F. Koksma, The theory of asymptotic distribution modulo one, Compositio Math. 16 (1964), 1-22. MR 30 #3874. MR 173664
- 8.
- M. Lerch, Question 1547, Intermédiaire Math. 11 (1904), 144-145.
- 9.
- W. M. Schmidt, Irregularities of distribution. VII, Acta Arith. 21 (1972), 45-50. MR 319933
- 10.
- D. C. Spencer, The lattice points of tetrahedra, J. Math. Phys. Mass. Inst. Tech. 21 (1942), 189-197. MR 4, 190. MR 7767
- 11.
- H. Weyl, Ueber ein Problem aus dem Gebiete der diophantischen Approximationen, Nachr. Ges. Wiss. Göttingen. Math.-Phys. Kl. 1914, 234-244; Gesammelte Abhandlungen. Band I, Springer-Verlag, Berlin and New York, 1968, pp. 487-497. MR 37 #6157.
- 12.
- H. Weyl, Sur une application de la théorie des nombres à la mécanique statistique et la théorie des perturbations, Enseignement Math. 16 (1914), 455-467. Gesammelte Abhandlungen, Band I, Springer-Verlag, Berlin and New York, 1968, pp. 498-510. MR 37 #6157.
- 13.
- H. Weyl, Ueber die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77 (1916) 313-352. Gesammelte Abhandlungen, Band I, Springer-Verlag, Berlin and New York, 1968, pp. 563-599. MR 37 #6157. MR 1511862
- 14.
- S. K. Zaremba (Ed.), Applications of number theory to numerical analysis, Academic Press, New York, 1972. MR 334452
Review Information:
Reviewer:
R. Tijdeman
Journal:
Bull. Amer. Math. Soc.
81 (1975), 672-675
DOI:
https://doi.org/10.1090/S0002-9904-1975-13818-3
