We study some classical identities for multiple zeta values and show that they still hold for zeta functions built from an arbitrary sequence of nonzero complex numbers. We introduce the complementary zeta function of a system, which naturally occurs when lifting identities for multiple zeta values to identities for quasisymmetric functions.

中文翻译：

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多个 zeta 值的结构特性

我们研究了多个 zeta 值的一些经典恒等式，并表明它们仍然适用于从任意非零复数序列构建的 zeta 函数。我们介绍互补 zeta 函数当将多个 zeta 值的恒等式提升为准对称函数的恒等式时，自然会发生这种情况。