Standard relations of multiple polylogarithm values at roots of unity

zbMath1197.11074arXiv0707.1459MaRDI QIDQ967732

Jianqiang Zhao

Publication date: 30 April 2010

Published in: Documenta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1459

zbMATH Keywords

regularizationdouble shuffle relationsmultiple polylogarithmsdistribution relationsstandard relations

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Zeta functions and (L)-functions of number fields (11R42) Polylogarithms and relations with (K)-theory (11G55) Higher logarithm functions (33B30) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (13)

Bachmann-Kühn's brackets and multiple zeta values at level \(N\) ⋮ Finite and symmetric colored multiple zeta values and multiple harmonic \(q\)-series at roots of unity ⋮ Analytic results for planar three-loop integrals for massive form factors ⋮ The parity theorem for multiple polylogarithms ⋮ Cyclic sum formula for multiple \(L\)-values ⋮ Alternating multiple \(T\)-values: weighted sums, duality, and dimension conjecture ⋮ Unit cyclotomic multiple zeta values for \(\mu_2, \mu_3\) and \(\mu_4\) ⋮ Analytic properties of multiple Dirichlet series associated to additive and Dirichlet characters ⋮ Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms ⋮ Multiple polylogarithm values at roots of unity ⋮ Evaluating multiple polylogarithm values at sixth roots of unity up to weight six ⋮ Restricted sum formula of alternating Euler sums ⋮ Some weighted sum formulas for multiple zeta, Hurwitz zeta, and alternating multiple zeta values

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