论文标题
数字有限的数字的加性属性
Additive properties of numbers with restricted digits
论文作者
论文摘要
在本文中，我们考虑了数字扩展受限制的整数的一些附加特性。令$ b \ geq 3 $是一个整数，$ b_b $是一组整数，其基础$ b $扩展只有数字$ \ {0,1 \}。$ \ $ \ $ a，b，b，c $是三个大于$ 2的整数大于2。 $（b_ {a}+b_ {b}）\ cap b_ {c} $在以下意义上是一个非常薄的集合，即对于每个$ε> 0，$ as as $ n \ to \ to \ infty，$ \ [ \＃（（b_ {a}+b_ {b}）\ cap b_ {c} \ cap [1，n]）= o（n^ε）。 \]
In this paper, we consider some additive properties of integers with restricted digit expansions. Let $b\geq 3$ be an integer and $B_b$ be the set of integers whose base $b$ expansions have only digits $\{0,1\}.$ Let $a,b,c$ be three integers greater than $2.$ We give some estimates on the size of $(B_{a}+B_{b})\cap B_{c}.$ In particular, under mild conditions, $(B_{a}+B_{b})\cap B_{c}$ is a very thin set in the following sense that for each $ε>0,$ as $N\to\infty,$ \[ \#((B_{a}+B_{b})\cap B_{c} \cap [1,N])=O(N^ε). \]
