论文标题
多个Zeta值对根林的概括
Generalisations of multiple zeta values to rooted forests
论文作者
论文摘要
我们表明，任何收敛的（洗牌）ARBORIFIED ZETA值都可以允许串联表示。这证明了对多个Zeta值的根系森林进行新的概括，我们研究了其代数特性。由于该系列表示，我们为Mordell-Tornheim Zeta值提供了Bradley和Zhou的某些结果的基本证据，并提供了明确的公式。洗牌的序列表示Zeta值也意味着它们是圆锥形Zeta值。我们表征了哪些圆锥形Zeta值是将ZETA值的，并将其评估为具有有理系数的多个Zeta值的总和。
We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a consequence of the series representation, we derive elementary proofs of some results of Bradley and Zhou for Mordell-Tornheim zeta values and give explicit formulas. The series representation for shuffle arborified zeta values also implies that they are conical zeta values. We characterise which conical zeta values are arborified zeta values and evaluate them as sums of multiple zeta values with rational coefficients.
