A law of the iterated logarithm for arithmetic functions

DOI10.1090/S0002-9939-06-08557-1zbMath1122.60030MaRDI QIDQ3420107

Michel J. G. Weber, István Berkes

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

strong law of large numbersiterated logarithmstrongly additive functionweighted sums of iid random variables

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (6)

On the law of large numbers and arithmetic functions ⋮ On the strong law of large numbers and additive functions ⋮ Small divisors of Bernoulli sums ⋮ Upper-lower class tests for weighted i.i.d. sequences and martingales ⋮ A law of large numbers for arithmetic functions ⋮ Lois du logarithme itéré avec pondérations additives

Cites Work

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• On the order of magnitude of the divisor function
• DISTRIBUTION FUNCTIONS OF ADDITIVE ARITHMETIC FUNCTIONS
• Convergence of weighted averages of independent random variables
• Mixing sequences of random variables and probablistic number theory
• On the Distribution of Additive Number-Theoretic Functions

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