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PreprintarXiv licencearXiv

Monotonicity of Coefficients of Interpolated Multiple Zeta Values

  • Shuji Yamamoto
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Abstract

Let ζt(k)=∑d=1rSd(k)tr−d be the interpolated multiple zeta value of an admissible index k of depth r. We show the monotonicity property of coefficients S1(k)≥⋯≥ Sr(k)>0. In the proof, we represent the coefficients as integrals over a common measure space and compares the integrands pointwise. As consequences, we determine the sign and vanishing of ζ−1(k) and locate the zeros of ζt(k) in the closed unit disk.

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Cite

BibTeXRIS
BibTeX
@misc{yamamoto2026monotonicity,
  title = {{Monotonicity of Coefficients of Interpolated Multiple Zeta Values}},
  author = {Shuji Yamamoto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15376},
  eprint = {2610.15376},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15376},
}
RIS
TY  - UNPB
TI  - Monotonicity of Coefficients of Interpolated Multiple Zeta Values
AU  - Shuji Yamamoto
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15376
UR  - https://arxiv.org/abs/2610.15376
AB  - Let ζ^t(k)=∑_d=1^rS_d(k)t^r−d be the interpolated multiple zeta value of an admissible index k of depth r. We show the monotonicity property of coefficients S_1(k)≥⋯≥ S_r(k)>0. In the proof, we represent the coefficients as integrals over a common measure space and compares the integrands pointwise. As consequences, we determine the sign and vanishing of ζ^−1(k) and locate the zeros of ζ^t(k) in the closed unit disk.
ER  -