$p$-adic multiple zeta values of integer indices
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915886698332160 |
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| author | Fan, Ku-Yu |
| author_facet | Fan, Ku-Yu |
| contents | This paper concerns the $p$-adic multiple zeta values of integer indices that may contain zero or negative components. We introduce the admissibility and regularizability conditions for integer indices. We define the $p$-adic multiple zeta values associated with admissible integer indices to be finite rational linear combinations of $p$-adic multiple zeta values associated with admissible positive integer indices. We prove that the double shuffle relations, that is, the shuffle and stuffle product formulas, both hold for the values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $p$-adic multiple zeta values of integer indices Fan, Ku-Yu Number Theory 11M32 (Primary) 11S80, 33B30 (Secondary) This paper concerns the $p$-adic multiple zeta values of integer indices that may contain zero or negative components. We introduce the admissibility and regularizability conditions for integer indices. We define the $p$-adic multiple zeta values associated with admissible integer indices to be finite rational linear combinations of $p$-adic multiple zeta values associated with admissible positive integer indices. We prove that the double shuffle relations, that is, the shuffle and stuffle product formulas, both hold for the values. |
| title | $p$-adic multiple zeta values of integer indices |
| topic | Number Theory 11M32 (Primary) 11S80, 33B30 (Secondary) |
| url | https://arxiv.org/abs/2603.22923 |