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Classical and Quantum Dilogarithm Identities
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We then demonstrate how classical dilogarithm identities naturally emerge from quantum dilogarithm identities in local form in the semiclassical limit by applying the saddle point method.
Keywords: dilogarithm, quantum dilogarithm, cluster algebra. 
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     author = {Rinat M. Kashaev and Tomoki Nakanishi},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a101/}
}
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Rinat M. Kashaev; Tomoki Nakanishi. Classical and Quantum Dilogarithm Identities. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a101/

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