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arXiv · 1910.06927

A functional equation related to generalized entropies and the modular group

Daniel Bennequin·Juan Pablo Vigneaux
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Abstract

We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies. These transformations generate the modular group, and this fact plays a crucial role in solving the system. The method suggests a more general relation between conditional probabilities and arithmetic.

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Daniel Bennequin, Juan Pablo Vigneaux. 2020-03-04. A functional equation related to generalized entropies and the modular group. https://doi.org/10.1007/s00010-020-00717-2

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