Research Cite this article: Tempesta P. 2015 A theorem on the existence of trace-form generalized entropies. Proc. R. Soc. A 471: 20150165. http://dx.An analytic technique is proposed, which allows to generate many new examples of entropic functionals generalizing the standard Boltzmann-Gibbs entropy. Our approach is based on the existence of a grouptheoretical structure, which is intimately related with the notion of entropy, as clarified in recent work of the author. The new entropies

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... satisfy the first three Shannon-Khinchin axioms and are composable (at least in a weak sense). By combining them, multiparametric examples of entropies can be realized. As a by-product of the theory, entropic functionals related to the Riemann zeta function and other numbertheoretical functions are introduced.