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On Arithmetic Properties of Integers with Missing Digits I: Distribution in Residue Classes

✍ Scribed by Paul Erdős; Christian Mauduit; András Sárközy

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 337 KB
Volume: 70
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2229

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✦ Synopsis

Consider all the integers not exceeding x with the property that in the system number to base g all their digits belong to a given set D/[0, 1, ..., g, &1]. The distribution of these integers in residue classes to ``not very large'' moduli is studied. 1998 Academic Press SECTION 1 Throughout this paper we use the following notations: We denote by R, Z, and N the sets of the real numbers, integers and positive integers. We write l 1 (N)=log N, l 2 (N)=log log N, l 3 (N)=log log log N. If F(N)=O(G(N)), then we write F(N)< <G(N); if the implied constant depends on certain parameters :, ;, ... (but on no other parameters), then we write F(N)= O :, ;, ... (G(N)) and F(N)< < :, ;, ... G(N). We denote by |(n) the number of Article No. NT982229

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