The joint distribution of additive and complex-valued multiplicative functions

Antanas Laurinčikas

Acta Mathematica Universitatis Ostraviensis (2005)

  • Volume: 13, Issue: 1, page 35-46
  • ISSN: 1804-1388

Abstract

top
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.

How to cite

top

Laurinčikas, Antanas. "The joint distribution of additive and complex-valued multiplicative functions." Acta Mathematica Universitatis Ostraviensis 13.1 (2005): 35-46. <http://eudml.org/doc/35151>.

@article{Laurinčikas2005,
abstract = {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.},
author = {Laurinčikas, Antanas},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {additive function; characteristic transform; probability measure; multiplicative function; weak convergence; additive function; characteristic transform; probability measure; multiplicative function; weak convergence},
language = {eng},
number = {1},
pages = {35-46},
publisher = {University of Ostrava},
title = {The joint distribution of additive and complex-valued multiplicative functions},
url = {http://eudml.org/doc/35151},
volume = {13},
year = {2005},
}

TY - JOUR
AU - Laurinčikas, Antanas
TI - The joint distribution of additive and complex-valued multiplicative functions
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2005
PB - University of Ostrava
VL - 13
IS - 1
SP - 35
EP - 46
AB - 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.
LA - eng
KW - additive function; characteristic transform; probability measure; multiplicative function; weak convergence; additive function; characteristic transform; probability measure; multiplicative function; weak convergence
UR - http://eudml.org/doc/35151
ER -

References

top
  1. Bakštys A., On limit distribution laws for arithmetic multiplicative functions, , Liet. matem. rink., 8 (1968), 5–20 (in Russian). (1968) 
  2. Delange H., On the distribution modulo 1 of additive functions, , J. Indian Math. Soc., 39 (1970), 215–235. (1970) MR0491576
  3. Delange H., Sur la distribution des valeurs des fonctions multiplicative complexes, , C. R. Acad. Sc. Paris, 276, Série A (1973), 161–164. (1973) MR0369302
  4. Erdös P., 10.1112/jlms/s1-13.2.119, , III, J. London Math. Soc. 13 (1938), 119–127. (1938) DOI10.1112/jlms/s1-13.2.119
  5. Erdös P., 10.1090/S0002-9904-1946-08604-8, , Bull. Amer. Math. Soc., 52 (1946), 527–537. (1946) MR0016078DOI10.1090/S0002-9904-1946-08604-8
  6. Erdös P. A. Wintner, 10.2307/2371326, , Amer. J. Math. 61 (1939), 713–721. (1939) MR0000247DOI10.2307/2371326
  7. Halász G., 10.1007/BF01894515, , Acta Math. Sci. Hung., 19(1968), 365–403. (1968) MR0230694DOI10.1007/BF01894515
  8. Laurinčikas A., On joint value distribution of additive and multiplicative functions, , Liet. matem. rink., 16(2)(1976), 190–192 (in Russian). (1976) 
  9. Laurinčikas A., On joint distribution of values of arithmetical functions, , Liet. matem. rink., 31(3)(1991), 433–454 (in Russian). (1991) MR1162237
  10. Laurinčikas A., Limit Theorems for the Riemann Zeta-Function, , Kluwer, Dordrecht, Boston, London, 1996. (1996) MR1376140
  11. Laurinčikas A., The joint distribution of the Riemann zeta-function, , 2005, submitted. MR2217939
  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). (1971) MR0302596
  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). (1973) MR0314790

NotesEmbed ?

top

You must be logged in to post comments.