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Signaling to relativistic observers: an Einstein-Shannon-Riemann encounter. (English. Russian original) Zbl 1459.94080

Probl. Inf. Transm. 56, No. 4, 303-308 (2020); translation from Probl. Peredachi Inf. 56, No. 4, 3-9 (2020).
Summary: A communication scenario is described involving a series of events triggered by a transmitter and observed by a receiver experiencing relativistic time dilation. The message selected by the transmitter is assumed to be encoded in the events’ timings and is required to be perfectly recovered by the receiver, regardless of the difference in clock rates in the two frames of reference. It is shown that the largest proportion of the space of all \(k\)-event signals that can be selected as a code ensuring error-free information transfer in this setting equals \(\zeta (k)^{-1}\), where \(\zeta\) is the Riemann zeta function.

MSC:

94A24 Coding theorems (Shannon theory)
94A05 Communication theory
94B99 Theory of error-correcting codes and error-detecting codes
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
11M41 Other Dirichlet series and zeta functions
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References:

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