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arXiv · 1612.09407

An equivalence between desingularized and renormalized values of multiple zeta functions at negative integers

Nao Komiyama
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Abstract

It is known that the special values of multiple zeta functions at non-positive arguments are indeterminate in most cases due to the occurrences of infinitely many singularities. In order to give a suitable rigorous meaning of the special values there, Furusho, Komori, Matsumoto and Tsumura introduced the desingularized values by the desingularization method to resolve all singularities. While, Ebrahimi-Fard, Manchon and Singer introduced the renormalized values to keep the "shuffle" relation by the renormalization procedure \`a la Connes and Kreimer. In this paper, we reveal an equivalence, that is, an explicit interrelationship between these two values. As a corollary, we also obtain an explicit formula to describe renormalized values in terms of Bernoulli numbers.

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Nao Komiyama. 2016-12-30. An equivalence between desingularized and renormalized values of multiple zeta functions at negative integers. https://arxiv.org/abs/1612.09407

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