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Hyper-Mahler measures via Goncharov-Deligne cyclotomy
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Hyper-Mahler measures via Goncharov-Deligne cyclotomy
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The hyper-Mahler measures $m_k( 1+x_1+x_2),k\in\mathbb Z_{>1}$ and $m_k( 1+x_1+x_2+x_3),k\in\mathbb Z_{>1}$ are evaluated in closed form via Goncharov-Deligne periods, namely $\mathbb Q$-linear combinations of multiple polylogarithms at cyclotomic points (complex-valued coordinates that are roots of unity). Some infinite series related to these hyper-Mahler measures are also explicitly represented as Goncharov-Deligne periods of levels $1$, $2$, $ 3$, $4$, $6$, $8$, $10$ and $12$.
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Cited by 1 Pith paper
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Multiple Clausen values and deformed Ap\'ery-like series
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