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PreprintCC BY 4.0arXiv

Multiple zeta values in λ-rings

  • Sergey Mozgovoy
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Abstract

We propose a framework for multiple zeta values in λ-rings that unifies both classical multiple zeta values and multiple q-zeta values. As in the classical case, we show that the multiple zeta function defines an algebra homomorphism from the quasi-shuffle algebra to the λ-ring. We also prove a formula for multiple polylogarithms in λ-rings, similar to the iterated integral expression in the classical case. As an application, we explicitly describe the algebra of regular multiple q-zeta values, compute the corresponding Poincaré series, and exhibit a small spanning set.

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Cite

BibTeXRIS
BibTeX
@misc{mozgovoy2026multiple,
  title = {{Multiple zeta values in $λ$-rings}},
  author = {Sergey Mozgovoy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04424},
  eprint = {2609.04424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04424},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Multiple zeta values in λ-rings
AU  - Sergey Mozgovoy
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04424
UR  - https://arxiv.org/abs/2609.04424
AB  - We propose a framework for multiple zeta values in λ-rings that unifies both classical multiple zeta values and multiple q-zeta values. As in the classical case, we show that the multiple zeta function defines an algebra homomorphism from the quasi-shuffle algebra to the λ-ring. We also prove a formula for multiple polylogarithms in λ-rings, similar to the iterated integral expression in the classical case. As an application, we explicitly describe the algebra of regular multiple q-zeta values, compute the corresponding Poincaré series, and exhibit a small spanning set.
ER  -