An almost-sure estimate for the mean of generalized -multiplicative functions of modulus
Jean-Loup Mauclaire (2000)
Journal de théorie des nombres de Bordeaux
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Let , be a Cantor scale, the compact projective limit group of the groups , identified to , and let be its normalized Haar measure. To an element , of we associate the sequence of integral valued random variables . The main result of this article is that, given a complex -multiplicative function of modulus , we have