Interpolant of truncated multiple zeta functions

Kentaro Ihara; Yayoi Nakamura; Shuji Yamamoto

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arXiv · 2407.20509

Interpolant of truncated multiple zeta functions

Kentaro Ihara·Yayoi Nakamura·Shuji Yamamoto

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Abstract

We introduce an analytic function $\Psi(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $\zeta_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using this expression, give the analytic continuation. Further, the harmonic product relations for $\Psi$ and $G$ are established via relevant Hopf algebra structures, and some properties of the function $G$ are provided.

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Kentaro Ihara, Yayoi Nakamura, Shuji Yamamoto. 2024-07-30. Interpolant of truncated multiple zeta functions. https://arxiv.org/abs/2407.20509

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