On the binary digits of a power

[摘要] Let B(m) denote the number of ones in the binary expansion of an integer m greater than or equal to 2. We prove that lim sup(m --> infinity)B(m(h))/log(2) m = h for integers h greater than or equal to 2. We also prove the same result with m(h) replaced by any polynomial a(0)m(h) + a(1)m(h-1) +...+ a(h) with integer coefficients and a(0) > 0. (C) 1997 Academic Press.

[发布日期] 1997-08-01