Minimum and maximum order of magnitude of the discrepancy of (nα)

C. Baxa, J. Schoissengeier
1994 Acta Arithmetica  
It is a classical result of P. Bohl [5], W. Sierpiński [21, 22] and H. Weyl [25, 26] that the sequence (nα) n≥1 is uniformly distributed modulo 1 if and only if α is irrational. The discrepancies
doi:10.4064/aa-68-3-281-290 fatcat:btp5qukctvhu7dtprxe4vumkqu