斯托纳姆数

斯托纳姆数Stoneham numbers)是一种特别的实数,得名自数学家李查·斯托纳姆(Richard G. Stoneham, 1920–1996)。对于互质且大于1的整数bc,可以定义斯托纳姆数αb,c 如下:

斯托纳姆在1973年证明只要c为奇质数,而bc2原根,则斯托纳姆数是以b为底的正规数

参考资料

  • Bugeaud, Yann. Distribution modulo one and Diophantine approximation. Cambridge Tracts in Mathematics 193. Cambridge: Cambridge University Press. 2012. ISBN 978-0-521-11169-0. Zbl 1260.11001. 
  • Stoneham, R.G. On absolute $(j,ε)$-normality in the rational fractions with applications to normal numbers. Acta Arithmetica. 1973, 22: 277–286. Zbl 0276.10028. 
  • Stoneham, R.G. On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers. Acta Arithmetica. 1973, 22: 371–389. Zbl 0276.10029.