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On the Joint Distribution ofq-Additive Functions in Residue Classes

✍ Scribed by Dong-Hyun Kim

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 204 KB
Volume: 74
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2327

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✦ Synopsis

Let S q (n) denote the sum of digits of n in base q. For given pairwise coprime bases q 1 , ..., q l and arbitrary residue classes a i mod m i (i=1, ..., l), we obtain an estimate with error term O(N 1&$ ) for the quantity

which extends results of J. Be sineau and establishes a conjecture of A. O. Gelfond. More generally, we obtain estimate of this type with each S q i replaced by an arbitrary integer-valued completely q i -additive function.

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