On mean values of random multiplicative functions
Résumé
Let P denote the set of primes and {f (p)} p∈P be a sequence of independent Bernoulli random variables taking values ±1 with probability 1/2. Extending f by multiplicativity to a random multiplicative function f supported on the set of squarefree integers, we prove that, for any ε > 0, the estimate nx f (n) √ x (log log x) 3/2+ε holds almost surely—thus qualitatively matching the law of iterated logarithm, valid for independent variables. This improves on corresponding results by Wintner, Erd˝ os and Halász .
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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