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 ζ(k)⁻¹, where ζ is the Riemann zeta function.

中文翻译：

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向相对论观察者发信号：爱因斯坦-香农-黎曼遭遇

描述了一种通信场景，该场景涉及一系列事件，这些事件由发射机触发，并且经历相对论时间膨胀的接收机观察到。假定发送器选择的消息是在事件的定时中编码的，并且要求接收器完美地恢复，而不管两个参考帧中时钟速率的差异如何。结果表明，在此设置下，可以选择作为确保无错信息传递的代码的所有k个事件信号中，最大的空间比例等于ζ（k）^-1，其中ζ是黎曼zeta函数。