This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations () and our recent results on combinatorial aspects of zeta functions on several variables.
In particular, we describe the action of the differential Galois group of on the asymptotic expansions of its solutions leading to a group of associators which contains the unique Drinfel’d associator (or Drinfel’d series). Non trivial expressions of an associator with rational coefficients are also explicitly provided, based on the algebraic structure and the singularity analysis of the multi-indexed polylogarithms and harmonic sums.
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Keywords: Algebraic Basis, Combinatorial Hopf Algebra, Harmonic Sum, Polylogarithm, Polyzeta
@article{CML_2019__11_2_25_0, author = {Hoang Ngoc Minh, Vincel}, title = {On the solutions of the universal differential equation with three regular singularities {(On} solutions of $KZ_3$)}, journal = {Confluentes Mathematici}, pages = {25--64}, publisher = {Institut Camille Jordan}, volume = {11}, number = {2}, year = {2019}, doi = {10.5802/cml.59}, language = {en}, url = {http://www.numdam.org/articles/10.5802/cml.59/} }
TY - JOUR AU - Hoang Ngoc Minh, Vincel TI - On the solutions of the universal differential equation with three regular singularities (On solutions of $KZ_3$) JO - Confluentes Mathematici PY - 2019 SP - 25 EP - 64 VL - 11 IS - 2 PB - Institut Camille Jordan UR - http://www.numdam.org/articles/10.5802/cml.59/ DO - 10.5802/cml.59 LA - en ID - CML_2019__11_2_25_0 ER -
%0 Journal Article %A Hoang Ngoc Minh, Vincel %T On the solutions of the universal differential equation with three regular singularities (On solutions of $KZ_3$) %J Confluentes Mathematici %D 2019 %P 25-64 %V 11 %N 2 %I Institut Camille Jordan %U http://www.numdam.org/articles/10.5802/cml.59/ %R 10.5802/cml.59 %G en %F CML_2019__11_2_25_0
Hoang Ngoc Minh, Vincel. On the solutions of the universal differential equation with three regular singularities (On solutions of $KZ_3$). Confluentes Mathematici, Volume 11 (2019) no. 2, pp. 25-64. doi : 10.5802/cml.59. http://www.numdam.org/articles/10.5802/cml.59/
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