The article presents a brief overview of the new direction in the theory of computing of functions represented by divergent series, for example, the Riemann zeta functions based on the use of physical analogy. For this, the notion of a relativistic Turing machine (RMT) is used, which has the same elements as its classic counterpart.The role of its head plays a material particle moving in accordance with the laws of relativistic mechanics along the numerical continuum playing the role of an RMT tape and having a nonEuclidean metric, the character of which depends on the calculation.Within this direction, evidence was obtained of the famous Riemann hypothesis.