Sur les entiers dont la somme des chiffres est moyenne

✍ Scribed by E. Fouvry; C. Mauduit

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 224 KB
• Volume: 114
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2005.03.007

✦ Synopsis

The goal of this paper is to study sets of integers with an average sum of digits. More precisely, let g be a fixed integer, s(n) be the sum of the digits of n in basis g. Let f : N → N such that, in any interval [g , g +1 [, f (n) is constant and near from (g -1) /2. We give an asymptotic for the number of integers n < x such that s(n) = f (n) and we prove that for every irrational the sequence ( n) is equidistributed mod 1, for n satisfying s(n) = f (n).