Possible connection between g(x) and
Fibonacci numbers?
Carlos Castro (Perelman), in his
recent article "pAdic
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.
This is of particular interest as the Golden Mean 1.618..., which is
intimately connected to the Fibonacci and binary Fibonacci sequences, has
been revealing itself as somehow relevant to the theory of the Riemann zeta
function in the recent works of Castro, Mahecha, Selvam, and Pitk&aum;nen.
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