论文标题
关于默森纳数字的数字
On digits of Mersenne numbers
论文作者
论文摘要
由最近发展的兴趣，以分配$ q $ - 元的数字$ m_p = 2^p-1 $，其中$ p $是Prime，我们估计使用$ m_p $，$ p \ leq x $，modulo，modulo的大量固定奇数prime $ q $。反过来，这立即意味着大约$（\ log x）^{3/2+o（1）} $ $ m_p $，$ p \ leq x $的最大数字。先前的结果暗示这仅对$（\ log x）^{1+o（1）} $最右边的数字。
Motivated by recently developed interest to the distribution of $q$-ary digits of Mersenne numbers $M_p = 2^p-1$, where $p$ is prime, we estimate rational exponential sums with $M_p$, $p \leq X$, modulo a large power of a fixed odd prime $q$. In turn this immediately implies the normality of strings of $q$-ary digits amongst about $(\log X)^{3/2+o(1)}$ rightmost digits of $M_p$, $p \leq X$. Previous results imply this only for about $(\log X)^{1+o(1)}$ rightmost digits.
