New representations for the Madelung constant.
On the evaluation of Euler sums.
Random generators and normal numbers.
On the random character of fundamental constant expansions.
On the binary expansions of algebraic numbers
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real has algebraic degree , then the number of 1-bits in the expansion of through bit position satisfies for a positive number (depending on ) and sufficiently large . This in itself establishes the transcendency of a class of...
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