A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918133714911232 |
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| author | Burmester, Annika |
| author_facet | Burmester, Annika |
| contents | We present the $τ$-invariant balanced quasi-shuffle algebra $\mathcal{G}^{\operatorname{f}}$, whose elements formalize (combinatorial) multiple Eisenstein series as well as multiple q-zeta values. In particular, $\mathcal{G}^{\operatorname{f}}$ has natural maps into these two algebras, and we expect these maps to be isomorphisms. Racinet studied the algebra $\mathcal{Z}^f$ of formal multiple zeta values by examining the corresponding affine scheme DM. Similarly, we present the affine scheme BM corresponding to the algebra $\mathcal{G}^{\operatorname{f}}$. We show that Racinet's affine scheme DM embeds into our affine scheme BM. This leads to a projection from the algebra $\mathcal{G}^{\operatorname{f}}$ onto $\mathcal{Z}^f$. Via the above natural maps, this projection corresponds to extracting the constant terms of multiple Eisenstein series or the limit $q\to1$ of multiple q-zeta values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02370 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values Burmester, Annika Number Theory Combinatorics Quantum Algebra 11M32, 16T05, 05A30 We present the $τ$-invariant balanced quasi-shuffle algebra $\mathcal{G}^{\operatorname{f}}$, whose elements formalize (combinatorial) multiple Eisenstein series as well as multiple q-zeta values. In particular, $\mathcal{G}^{\operatorname{f}}$ has natural maps into these two algebras, and we expect these maps to be isomorphisms. Racinet studied the algebra $\mathcal{Z}^f$ of formal multiple zeta values by examining the corresponding affine scheme DM. Similarly, we present the affine scheme BM corresponding to the algebra $\mathcal{G}^{\operatorname{f}}$. We show that Racinet's affine scheme DM embeds into our affine scheme BM. This leads to a projection from the algebra $\mathcal{G}^{\operatorname{f}}$ onto $\mathcal{Z}^f$. Via the above natural maps, this projection corresponds to extracting the constant terms of multiple Eisenstein series or the limit $q\to1$ of multiple q-zeta values. |
| title | A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values |
| topic | Number Theory Combinatorics Quantum Algebra 11M32, 16T05, 05A30 |
| url | https://arxiv.org/abs/2307.02370 |