We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, considering Zaremba’s set modulo p , that is the set of all a such that $${a \over p} = [{a_1}, \ldots ,{a_s}]$$ a p = [ a 1 , … , a s ] has bounded partial quotients, a j ⩽ M , we obtain a sharp upper bound for the cardinality of this set.

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热门产品和连分数

我们证明了具有弱加性结构的集合的乘积流行的界限，并使用这些界限来证明关于连分数的结果。即，考虑到 Zaremba 的集合模 p ，即所有 a 的集合使得 $${a \over p} = [{a_1}, \ldots ,{a_s}]$$ ap = [ a 1 , … , as ]有界部分商，aj ⩽ M ，我们获得了这个集合的基数的一个尖锐的上界。