Carlos Castro (Perelman), in his recent article "p-Adic stochastic dynamics, supersymmetry and the Riemann conjecture", points out that the function

also appears in the theory of the binary Fibonacci sequence (sometimes known as the Golden String).

Apparently, on page 310 of M. Schroeder's recent book Fractals, Chaos, Power Laws, the author notes that if treated as a square wave form, the binary Fibonacci sequence produces a Fourier amplitude spectrum involving this function.

This may be purely coincidental, but as far as I am aware, no one has seriously considered the possible connections between the binary Fibonacci sequence, the zeros of the Riemann zeta function, and random matrix theory that it suggests.