论文标题
sur larépartitionintime de la repredsentation d'ostrowski dan dan les les class derésidue
Sur la répartition jointe de la représentation d'Ostrowski dans les classes de résidue
论文作者
论文摘要
对于两个不同的整数$ m_1，m_2 \ ge2 $，我们设置$α_1= [0; \ edline {1，m_1}] $和$α_2= [0; \ overline {1，m_2}] $，我们用$ s_ {α_1} $和$ s__2}表示naime n aughtlline {1，m_1}] $ and $ s_2} $ s_ {n）naime和$ s_2} ostrowski $α_1$和$α_2-$表示$ n $。令$ b_1，b_2 $为正整数满足$（b_1，m_1）= 1 $和$（b_2，m_2）= 1 $，我们获得了一个错误项$ o（n^{1-Δ}）$的估计，用于以下$ \ big \ big \ \ \ \ leq n <n <n < a_1 \ pmod {b_1}，\ s_ {α_2}（n）\ equiv a_2 \ pmod {b_2} \ big \}，所有整数$ a_1 $ and $ a_2。$ a _1 $ and $ a_2。$ $ $应与Bésineau和kim copeans copire copire and $ q- $ q- $ q- $ q- $ q- $ q- $ q- $ q- $ q- q-进行比较。
For two distinct integers $m_1,m_2\ge2$, we set $α_1=[0;\overline{1,m_1}]$ and $α_2=[0;\overline{1,m_2}]$ and we denote by $S_{α_1}(n)$ and $S_{α_2}(n)$ respectively the sum of digits functions in the Ostrowski $α_1$ and $α_2-$representations of $n$. Let $b_1,b_2 $ be positive integers satisfying $(b_1,m_1)=1$ and $(b_2,m_2)=1$, we obtain an estimation with an error term $O(N^{1-δ})$ for the cardinal of the following set $$\Big\{ 0\leq n<N;\ S_{α_1}(n)\equiv a_1\pmod{b_1},\ S_{α_2}(n)\equiv a_2\pmod{b_2}\Big\},$$ for all integers $a_1$ and $a_2.$ Our result should be compared to that of Bésineau and Kim who treated the case of the $q-$representations in different bases (that are coprimes).
