57
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Extremality Properties of Some Diophantine Series

Pages 481-494 | Received 07 Jul 2009, Accepted 20 Oct 2009, Published online: 23 Feb 2011

REFERENCES

  • Baxa , C. 2000 . “Comparing the Distribution of (nα)-Sequences.” . Acta Arith. , 94 : 345 – 363 . [Baxa 00]
  • Cusick , T. W. and Flahive , M. E. 1989 . The Markoff and Lagrange Spectra , Mathematical Surveys and Monographs 30 Providence : American Mathematical Society. . [Cusick and Flahive 89]
  • de la Bretèche , R. and Tenenbaum , G. 2004 . “Séries trigonométriques à coefficients arithmétiques.” . J. Anal. Math. , 92 : 1 – 79 . [de la Bretèche and Tenenbaum 04]
  • Dupain , Y. and Sós , V. T. 1984 . “On the Discrepancy of (nα) Sequences.” . In Topics in Classical Number Theory Vols. I , 355 – 387 . Amsterdam : North-Holland. . II (Budapest, 1981), Colloq. Math. Soc. Jáanos Bolyai 34, [Dupain and Sós 84]
  • Jager , H. and de Jonge , J. 1994 . “The Circular Dispersion Spectrum.”. . J. Number Theory , 49 ( 3 ) : 360 – 384 . [Jager and de Jonge 94]
  • Khintchine , Ya. A. 1997 . Continued Fractions New York : Dover. . [Khintchine 97]
  • Kruse , A. H. 1966/1967 . “Estimates of ΣNk=1 k−s〈kx〉−t” . Acta Arith. , 12 : 229 – 261 . [Kruse 66]
  • Martin , B. 2007 . “Nouvelles identités de Davenport.” . Functiones et Approximatio , 37 ( 2 ) : 293 – 328 . [Martin 07]
  • Niederreiter , H. 1984 . “On a Measure of Denseness for Sequences.” . In Topics in Classical Number Theory Vols. I , 1163 – 1208 . Amsterdam : North-Holland. . II (Budapest, 1981), Colloq. Math. Soc. János Bolyai 34, [Niederreiter 84]
  • Rivoal , T. 2008 . “On the Distribution of Multiples of Real Numbers.” Available at http://hal.archives-ouvertes.fr/hal-00526980/fr[Rivoal 08] Preprint
  • Schoissengeier , J. 2007 . “On the Convergence of a Series of Bundschuh.” . Uniform Distribution Theory , 2 ( 1 ) : 107 – 133 . [Schoissengeier 07]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.