ON RANDOM ARITHMETICAL FUNCTIONS. I

被引：1

作者：

Indlekofer, K. -H. ^{[1
]}

Katai, I. ^{[2
]}

Klesov, O. I. ^{[3
]}

机构：

[1] Univ Gesamthsch Paderborn, Fac Math & Informat, D-33098 Paderborn, Germany

[2] Eotvos Lorand Univ, Dept Comp Algebra, H-1117 Budapest, Hungary

[3] Natl Tech Univ Ukraine KPI, Dept Math Anal & Probabil Theory, UA-03056 Kiev, Ukraine

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2010年 / 50卷 / 03期

关键词：

multiplicative functions; mean-value theorem; MULTIPLICATIVE FUNCTIONS;

D O I：

10.1007/s10986-010-9085-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A(Q) be the group of complex unit roots of an integer order Q >= 2. Let xi(p) (p epsilon P) be independent random variables distributed uniformly on the set A(Q), where P is the set of primes. Let f be a completely multiplicative function defined on P by f(p) = xi(p). We investigate the summatory function of f(n) and the density of those n for which f(n + j) = kappa(j) (j = 0,...,t), where kappa(j) A(Q).

引用

下载

页码：271 / 283

页数：13

共 50 条

[1] On random arithmetical functions. I
K.-H. Indlekofer
I. Kátai
O.I. Klesov
Lithuanian Mathematical Journal, 2010, 50 : 271 - 283
[2] Arithmetical periodicities of Bessel functions.
Lehmer, DH
ANNALS OF MATHEMATICS, 1932, 33 : 143 - 150
[3] A characterization of some additive arithmetical functions. V
J. L. Mauclaire
Acta Mathematica Hungarica, 2002, 96 : 327 - 340
[4] Arithmetical characteristic of series development of rational functions.
Polya, HG
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1921, 151 (1/4): : 1 - 31
[5] A characterization of some additive arithmetical functions. V
Mauclaire, JL
ACTA MATHEMATICA HUNGARICA, 2002, 96 (04) : 327 - 340
[6] DISCRETE REPRESENTATIONS OF SECOND ORDER RANDOM FUNCTIONS. I
Ponomarenko, O. I.
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS, 2012, 86 : 163 - 171
[7] On Polynomial Random Functions.
Stanasila, Tatiana
Buletinul Institutului Politehnic Gheorghe Gheorghiu-Dej Bucuresti. Seria electrotehnica, 1982, 44 (03): : 3 - 8
[8] On certain finitely solvable equations between arithmetical functions.
Bell, ET
AMERICAN JOURNAL OF MATHEMATICS, 1929, 51 : 47 - 50
[9] Random relations, random utilities, and random functions.
Regenwetter, M
Marley, AAJ
JOURNAL OF MATHEMATICAL PSYCHOLOGY, 1996, 40 (04) : 360 - 360
[10] Mathematical analysis - On some arithmetical consequences of the theory of abelian functions.
Humbert, G
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1906, 142 : 537 - 541

← 1 2 3 4 5 →