Some applications of Franel-Kluyver's integral. II.

Oto Strauch

Mathematica Slovaca (1989)

  • Volume: 39, Issue: 2, page 127-140
  • ISSN: 0232-0525

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Strauch, Oto. "Some applications of Franel-Kluyver's integral. II.." Mathematica Slovaca 39.2 (1989): 127-140. <http://eudml.org/doc/31910>.

@article{Strauch1989,
author = {Strauch, Oto},
journal = {Mathematica Slovaca},
keywords = {Franel-Kluyver's integral; square of greatest common divisor; convergent infinite series; uniform distribution; Bernoulli number; speed of convergence},
language = {eng},
number = {2},
pages = {127-140},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Some applications of Franel-Kluyver's integral. II.},
url = {http://eudml.org/doc/31910},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Strauch, Oto
TI - Some applications of Franel-Kluyver's integral. II.
JO - Mathematica Slovaca
PY - 1989
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 39
IS - 2
SP - 127
EP - 140
LA - eng
KW - Franel-Kluyver's integral; square of greatest common divisor; convergent infinite series; uniform distribution; Bernoulli number; speed of convergence
UR - http://eudml.org/doc/31910
ER -

References

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  1. FRANEL J., Les suites de Farey et le problème des nombres premiers, Göttinger Nachrichten, 1924, 198-201. (1924) 
  2. LANDAU E., Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel, Göttinger Nachrichten, 1924, 202-206. (1924) 
  3. LANDAU E., Vorlesung über Zahlentheoгie, Band 2. Verlag von S. Hirzel in Leipzig 1927. (1927) 
  4. KLUYVER J. C., An analytical expression for the greatest common divisor of two integers, Proceedings Royal Acad. Amsterdam, Vol. V, II, 1903, 658-662. (1903) 
  5. GÁL I. S., A theorem concerning diophantine approximations, Nieuw Arch. Wisk. 23, 1949, 13-38. (1949) Zbl0031.25601MR0027788
  6. KOKSMA J. F., On a certain integral in the theory of uniform distribution, Indag. Math. 13, 1951, 285-287. (1951) Zbl0043.27701MR0045165
  7. LE VEQUE W. J., On the frequency of small fractional parts in certain real sequences III, J. Reine Angew. Math. 202, 1959, 215-220. (1959) MR0121351
  8. STRAUCH O., Some new criterions for sequences which satisfy Duffin - Schacffer conjecture I, Acta Math. Univ. Comenian. 42-43, 1983, 87-95. (1983) MR0740736
  9. DYER T., HARMAN G., Sums involving common divisors, J. London Math. Soc. (2) 34, 1986, 1-11. (1986) Zbl0602.10041MR0859143
  10. KUIPERS L., NIEDERREITER H., Uniform Distribution of Sequences, J. Wiley New York 1974. (1974) Zbl0281.10001MR0419394
  11. KOKSMA J. F., A general theorem from the theory of uniform distribution modulo 1, Mathematica, Zutphen B11, 1942, 7-11. (1942) MR0015094
  12. KOKSMA J. F., Some integrals in the theory of uniform distribution modulo 1, Mathematica, Zutphen B11, 1942,49-52. (1942) MR0015095

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