| Title:
|
On weighted densities (English) |
| Author:
|
Giuliano-Antonini, Rita |
| Author:
|
Grekos, Georges |
| Author:
|
Mišík, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
947-962 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The continuity of densities given by the weight functions $n^{\alpha }$, $\alpha \in [-1,\infty [$, with respect to the parameter $\alpha $ is investigated. (English) |
| Keyword:
|
asymptotic density |
| Keyword:
|
logarithmic density |
| Keyword:
|
$f$-density |
| Keyword:
|
continuity |
| MSC:
|
11B05 |
| MSC:
|
11K09 |
| MSC:
|
11K99 |
| MSC:
|
11P70 |
| idZBL:
|
Zbl 1195.11018 |
| idMR:
|
MR2356932 |
| . |
| Date available:
|
2009-09-24T11:50:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128218 |
| . |
| Reference:
|
[1] A. Fuchs and R. Antonini Giuliano: Théorie générale des densités.Rend. Acc. Naz. delle Scienze detta dei XL, Mem. di Matematica, 108 (XIV, 14) (1990), 253–294. MR 1106580 |
| Reference:
|
[2] H. Halberstam and K. F. Roth: Sequences.Oxford Univ. Press, 1966. MR 0210679 |
| Reference:
|
[3] G. H. Hardy and M. Riesz: The General Theory of Dirichlet Series.Cambridge Univ. Press, 1952. |
| Reference:
|
[4] L. Mišík: Sets of positive integers with prescribed values of densities.Mathematica Slovaca 52 (2002), 289–296. MR 1936334 |
| Reference:
|
[5] L. Mišík and J. T. Tóth: Logarithmic density of a sequence of integers and density of its ratio set.Journal de Théorie des Nombres de Bordeaux 15 (2003), 309–318. MR 2019018, 10.5802/jtnb.404 |
| Reference:
|
[6] C. T. Rajagopal: Some limit theorems.Amer. J. Math. 70 (1948), 157–166. Zbl 0041.18301, MR 0023930, 10.2307/2371942 |
| . |
