Evaluating multiple polylogarithm values at sixth roots of unity up to weight six

DOI10.1016/j.nuclphysb.2017.03.026zbMath1361.81105arXiv1512.08389OpenAlexW2963188989MaRDI QIDQ529310

Vladimir A. Smirnov, Johannes M. Henn, Alexander V. Smirnov

Publication date: 18 May 2017

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.08389

Mathematics Subject Classification ID

Feynman diagrams (81T18) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Polylogarithms and relations with (K)-theory (11G55)

Related Items

Three-loop effective potential of general scalar theory via differential equations, Analytic results for planar three-loop integrals for massive form factors, Massive three-loop form factor in the planar limit, Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points, Two-loop diagrams in nonrelativistic QCD with elliptics, Higgs boson contribution to the leading two-loop Yukawa corrections to \(gg \rightarrow HH\), One-loop hexagon integral to higher orders in the dimensional regulator, Subleading power resummation of rapidity logarithms: the energy-energy correlator in \(\mathcal{N} = 4\) SYM, Automated solution of first order factorizable systems of differential equations in one variable, Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes, Three-loop vertex integrals at symmetric point

Cites Work

• Unnamed Item
• The elliptic dilogarithm for the sunset graph
• The multiple zeta value data mine
• The unipotent motivic fundamental group of \(\mathbf G_m - \mu_N\), for \(N=2,3,4,6\) or \(8\)
• Numerical evaluation of multiple polylogarithms
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Standard relations of multiple polylogarithm values at roots of unity
• Multiple polylogarithms, cyclotomy and modular complexes
• A Feynman integral via higher normal functions
• Harmonic sums and polylogarithms generated by cyclotomic polynomials
• Groupes fondamentaux motiviques de Tate mixte
• Analysis of PSLQ, an integer relation finding algorithm
• HARMONIC POLYLOGARITHMS
• Derivation and double shuffle relations for multiple zeta values
• New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams