| Title:
|
The joint distribution of additive and complex-valued multiplicative functions (English) |
| Author:
|
Laurinčikas, Antanas |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
13 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
35-46 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper the necessary and sufficient conditions for the existence of joint limit distribution for real additive and complex-valued multiplicative function are presented. (English) |
| Keyword:
|
additive function |
| Keyword:
|
characteristic transform |
| Keyword:
|
probability measure |
| Keyword:
|
multiplicative function |
| Keyword:
|
weak convergence |
| MSC:
|
11N60 |
| idZBL:
|
Zbl 1207.11102 |
| idMR:
|
MR2290417 |
| . |
| Date available:
|
2009-12-29T09:16:57Z |
| Last updated:
|
2015-03-15 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137470 |
| . |
| Reference:
|
[1] Bakštys A.: On limit distribution laws for arithmetic multiplicative functions., Liet. matem. rink., 8 (1968), 5–20 (in Russian). |
| Reference:
|
[2] Delange H.: On the distribution modulo 1 of additive functions., J. Indian Math. Soc., 39 (1970), 215–235. MR 0491576 |
| Reference:
|
[3] Delange H.: Sur la distribution des valeurs des fonctions multiplicative complexes., C. R. Acad. Sc. Paris, 276, Série A (1973), 161–164. MR 0369302 |
| Reference:
|
[4] Erdös P.: On the density of some sequences of numbers., III, J. London Math. Soc. 13 (1938), 119–127. 10.1112/jlms/s1-13.2.119 |
| Reference:
|
[5] Erdös P.: Some remarks about additive and multiplicative functions., Bull. Amer. Math. Soc., 52 (1946), 527–537. MR 0016078, 10.1090/S0002-9904-1946-08604-8 |
| Reference:
|
[6] Erdös P. A. Wintner: Additive arithmetical functions and statistical independence., Amer. J. Math. 61 (1939), 713–721. MR 0000247, 10.2307/2371326 |
| Reference:
|
[7] Halász G.: Über die Mittelwerte multikativer zahlentheoreticher Funktionen., Acta Math. Sci. Hung., 19(1968), 365–403. MR 0230694, 10.1007/BF01894515 |
| Reference:
|
[8] Laurinčikas A.: On joint value distribution of additive and multiplicative functions., Liet. matem. rink., 16(2)(1976), 190–192 (in Russian). |
| Reference:
|
[9] Laurinčikas A.: On joint distribution of values of arithmetical functions., Liet. matem. rink., 31(3)(1991), 433–454 (in Russian). MR 1162237 |
| Reference:
|
[10] Laurinčikas A.: Limit Theorems for the Riemann Zeta-Function., Kluwer, Dordrecht, Boston, London, 1996. MR 1376140 |
| Reference:
|
[11] Laurinčikas A.: The joint distribution of the Riemann zeta-function., 2005, submitted. MR 2217939 |
| Reference:
|
[12] Levin B. V., Timofeev N. M.: Analytic method in probabilistic number theory., Uch. zap. Vladim. gos. ped. inst., 57(2) (1971), 57–150 (in Russian). MR 0302596 |
| Reference:
|
[13] Levin B. V., Timofeev N. M., Tuliaganov S. T.: Distribution of values of multiplicative functions., Liet. matem. rink., 13(1) (1973), 87–100 (in Russian). MR 0314790 |
| . |
