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arXiv · 1804.05568

Shuffle-type product formulae of desingularized values of multiple zeta-functions

Nao Komiyama
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Abstract

It is known that there are infinitely many singularities of multiple zeta functions and the special values at non-positive integer points are indeterminate. In order to give a suitable rigorous meaning of the special values there, Furusho, Komori, Matsumoto and Tsumura introduced desingularized values by using their desingularization method to resolve all singularities. On the other hand, Ebrahimi-Fard, Manchon and Singer introduced renormalized values by the renormalization method \`{a} la Connes and Kreimer and they showed that the values fulfill the shuffle-type product formula. In this paper, we show the shuffle-type product formulae for desingularized values.

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Nao Komiyama. 2018-04-16. Shuffle-type product formulae of desingularized values of multiple zeta-functions. https://arxiv.org/abs/1804.05568

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