On the decomposition of motivic multiple zeta values

By F. Brown. 2011

195 citations recorded by the source corpus.

We review motivic aspects of multiple zeta values, and as an ap- plication, we give an exact-numerical algorithm to decompose any (motivic) multiple zeta value of given weight into a chosen basis up to that weight.

Subfields: Algebra and Number Theory, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/6f6296957fe381aa542f9859c8c6376686472d75

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In Algebra and Number Theory

In Theoretical Computer Science

Citations in the corpus

SINGLE-VALUED MOTIVIC PERIODS AND MULTIPLE ZETA VALUES (2014, background): “The objects ζ (w) were denoted by ζ (w) in [10].”
Soft triple-real radiation for Higgs production at N3LO (2013, methodology): “[124] an algorithm was described that allows to reconstruct these zeta-valued terms using the full Hopf algebra structure of multiple polylogarithms, augmented by some ideas by Brown [125].”
Polylogarithms, multiple zeta values and superstring amplitudes (2013, background): “An introduction to the theory of motivic zeta values in the context of string theory amplitudes can be found in [12]; the original papers are [21, 39].”
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes (2012, background): “[58], augmented by some ideas inspired by a recent paper by Brown [59].”
Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series (2018, unknown): “The coaction acts trivially on iπ [13, 16],2 ∆MPL(iπ) = iπ ⊗ 1 .”
Mathematical aspects of scattering amplitudes (2014, unknown): “(96) on elements of H, while on iπ it acts by [30, 31] ∆(iπ) = iπ ⊗ 1 .”
Motivic multiple zeta values and superstring amplitudes (2012, background): “A generalization of the symbol approach is the coproduct structure of multiple polylogarithms [4,5].”
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2014, background): “The case u ∈ {0, 1} of multiple zeta values (MZV) is by now perfectly understood on the motivic level [35], such that conjectural Q-bases are available at arbitrary weight and [36] even provides a reduction algorithm that was implemented in [34].”
Mixed Tate motives over $\Z$ (2011, methodology): “These notations are useful for explicit computations, for which it can be convenient to vary the choice of map φ (see [2]).”
PolyLogTools — polylogs for the masses (2019, methodology): “582240526465012505902656320159680108746 Out[7]:= -Pi^2/12 + Log[2]^2/2 Out[8]:= -Pi^2/12 + Log[2]^2/2”
Single-valued harmonic polylogarithms and the multi-Regge limit (2012, methodology): “The result is a complicated expression involving multiple polylogarithms which can be matched to a combination of SVHPLs and zeta values by means of the symbol [20, 21, 22, 23, 24] and coproduct [59, 60, 61].”
Feynman integrals and hyperlogarithms (2015, methodology): “This can be achieved by the coproduct-based algorithm [56] which is available as a program [153].”