Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves

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The elliptic dilogarithm for the sunset graph (2013, methodology): “In this appendix we recall the main properties of the elliptic dilogarithms following [20, 39, 40].”
Multiple Elliptic Polylogarithms (2011, methodology): “xp(2πiτ). In order to construct multivalued functions on E×, the basic idea is to average a multivalued function on C× with respect to multiplication by q as was done for the classical polylogarithms [2, 13]. However, applying this idea naively to the multiple polylogarithms in one variable (1.4) do”
Motivic amplitudes and cluster coordinates (2013, background): “icted by the Freeness Conjecture [23]. We start from its low weight consequences. Weight 1. First of all, one has L 1(F) = F Z Q: (4.8) Weight 2. Let us recall the denition of the Bloch group B 2(F) [49,50]. Let Q[F] be the Q-vector space with basis elements fxgfor x2F. Recall the cross-ratio r(x 1;”
From polygons and symbols to polylogarithmic functions (2011, unknown): “e generalizations [1, 2] play an equally important role in modern mathematics and in physics. In mathematics they occur for instance in connection with algebraic K-theory and mixed Tate motives, e.g. [3, 4, 5, 6, 7, 8], with Hilbert’s third problem (on scissors congruences), e.g. [9, 10, 11], as vol”