Affiliation:
1. Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Lithuania
Abstract
For any A ? N, let U(A,N) be the number of its elements not exceeding N.
Suppose that A + A has V (A,N) elements not exceeding N, where the elements
in the sumset A + A are counted with multiplicities. We first prove a sharp
inequality between the size of U(A,N) and that of V (A,N) which, for the
upper limits ?(A) = lim supN?? U(A,N)N-1/2 and ? (A) = lim sup N?? V
(A,N)N-1, implies ?(A)2 ? 4 ? (A)/?. Then, as an application, we show that,
for any square-free integer d > 1 and any ? > 0, there are infinitely many
positive integers N such that at least (?8/ ?- ?) ?N digits among the first
N digits of the binary expansion of ?d are equal to 1.
Publisher
National Library of Serbia
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
1 articles.
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