Speaker: Gal Porat
(Hebrew University):
Title:
Asymptotically Uniform Period Distribution for Binary Expansions of Rational Numbers

Abstract:
The binary expansion of a rational number q is periodic, and if we choose at random k consecutive digits from a period, we see that q induces a probability measure on binary strings of length k. We show that there exists a density one sequence of primes, such that the sequence of measures induced by their reciprocals converges to the uniform measure for every k.

This result and some others are obtained by basic methods of Fourier analysis and analytic number theory, using results of Pappalardi and Kurlberg.

This is a joint work with Guy Kapon carried out under the supervision of Ofir David and Uri Shapira.