@article{MASLO_1989_39_2_a1,
author = {Strauch, Oto},
title = {Some applications of {Franel-Kluyver's} integral. {II}},
journal = {Mathematica slovaca},
pages = {127--140},
year = {1989},
volume = {39},
number = {2},
mrnumber = {1018254},
zbl = {0671.10002},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MASLO_1989_39_2_a1/}
}
Strauch, Oto. Some applications of Franel-Kluyver's integral. II. Mathematica slovaca, Tome 39 (1989) no. 2, pp. 127-140. http://geodesic.mathdoc.fr/item/MASLO_1989_39_2_a1/
[1] FRANEL J.: Les suites de Farey et le problème des nombres premiers. Göttinger Nachrichten, 1924, 198-201.
[2] LANDAU E.: Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel. Göttinger Nachrichten, 1924, 202-206.
[3] LANDAU E.: Vorlesung über Zahlentheoгie. Band 2. Verlag von S. Hirzel in Leipzig 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.
[5] GÁL I. S.: A theorem concerning diophantine approximations. Nieuw Arch. Wisk. 23, 1949, 13-38. | MR | Zbl
[6] KOKSMA J. F.: On a certain integral in the theory of uniform distribution. Indag. Math. 13, 1951, 285-287. | MR | Zbl
[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. | MR
[8] STRAUCH O.: Some new criterions for sequences which satisfy Duffin - Schacffer conjecture I. Acta Math. Univ. Comenian. 42-43, 1983, 87-95. | MR
[9] DYER T., HARMAN G.: Sums involving common divisors. J. London Math. Soc. (2) 34, 1986, 1-11. | MR | Zbl
[10] KUIPERS L., NIEDERREITER H.: Uniform Distribution of Sequences. J. Wiley New York 1974. | MR | Zbl
[11] KOKSMA J. F.: A general theorem from the theory of uniform distribution modulo 1. Mathematica, Zutphen B11, 1942, 7-11. | MR
[12] KOKSMA J. F.: Some integrals in the theory of uniform distribution modulo 1. Mathematica, Zutphen B11, 1942,49-52. | MR