| Title:
|
Some applications of Franel-Kluyver's integral. II. (English) |
| Author:
|
Strauch, Oto |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1989 |
| Pages:
|
127-140 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11A05 |
| MSC:
|
11J71 |
| idZBL:
|
Zbl 0671.10002 |
| idMR:
|
MR1018254 |
| . |
| Date available:
|
2009-09-25T10:16:20Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129943 |
| . |
| Reference:
|
[1] FRANEL J.: Les suites de Farey et le problème des nombres premiers.Göttinger Nachrichten, 1924, 198-201. |
| Reference:
|
[2] LANDAU E.: Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel.Göttinger Nachrichten, 1924, 202-206. |
| Reference:
|
[3] LANDAU E.: Vorlesung über Zahlentheoгie.Band 2. Verlag von S. Hirzel in Leipzig 1927. |
| Reference:
|
[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. |
| Reference:
|
[5] GÁL I. S.: A theorem concerning diophantine approximations.Nieuw Arch. Wisk. 23, 1949, 13-38. Zbl 0031.25601, MR 0027788 |
| Reference:
|
[6] KOKSMA J. F.: On a certain integral in the theory of uniform distribution.Indag. Math. 13, 1951, 285-287. Zbl 0043.27701, MR 0045165 |
| Reference:
|
[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 0121351 |
| Reference:
|
[8] STRAUCH O.: Some new criterions for sequences which satisfy Duffin - Schacffer conjecture I.Acta Math. Univ. Comenian. 42-43, 1983, 87-95. MR 0740736 |
| Reference:
|
[9] DYER T., HARMAN G.: Sums involving common divisors.J. London Math. Soc. (2) 34, 1986, 1-11. Zbl 0602.10041, MR 0859143 |
| Reference:
|
[10] KUIPERS L., NIEDERREITER H.: Uniform Distribution of Sequences.J. Wiley New York 1974. Zbl 0281.10001, MR 0419394 |
| Reference:
|
[11] KOKSMA J. F.: A general theorem from the theory of uniform distribution modulo 1.Mathematica, Zutphen B11, 1942, 7-11. MR 0015094 |
| Reference:
|
[12] KOKSMA J. F.: Some integrals in the theory of uniform distribution modulo 1.Mathematica, Zutphen B11, 1942,49-52. MR 0015095 |
| . |
