Motivic multiple zeta values relative to \(\mu_2\) (Q2219881)

The motivic multiple zeta values relative to \(\mu_{N}\) introduced in the works of \textit{F. Brown} [Ann. Math. (2) 175, No. 2, 949--976 (2012; Zbl 1278.19008)] and \textit{C. Glanois} [J. Number Theory 160, 334--384 (2016; Zbl 1398.14011)] have been studied in a number of papers. Restricting themselves to the \(\mu_{2}\) case, the authors obtain several interesting results, too technical to be cited here. In particular, reinterpreting the results of \textit{M. Kaneko} and \textit{K. Tasaka} [Math. Ann. 357, No. 3, 1091--1118 (2013; Zbl 1327.11059)] in the motivic setting, the authors prove Kaneko and Tasaka's conjectures about the sum odd double zeta values and the classical double zeta values, and an analogue of their conjecture in depth three. In conclusion, the authors formulate a conjecture, relating to the sum odd double zeta values in higher depth.