Multiple $\wp$-Functions and Their Applications
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911633966628864 |
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| author | Kanno, Hayato Kina, Katsumi |
| author_facet | Kanno, Hayato Kina, Katsumi |
| contents | In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single $\wp$-functions with coefficients given by multiple Eisenstein series. As an application, we derive some relations among multiple Eisenstein series and multiple zeta values by exploiting the double periodicity of the multiple $\wp$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple $\wp$-Functions and Their Applications Kanno, Hayato Kina, Katsumi Number Theory 11M32, 33E05 (Primary), 11F11 (Secondary) In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single $\wp$-functions with coefficients given by multiple Eisenstein series. As an application, we derive some relations among multiple Eisenstein series and multiple zeta values by exploiting the double periodicity of the multiple $\wp$-functions. |
| title | Multiple $\wp$-Functions and Their Applications |
| topic | Number Theory 11M32, 33E05 (Primary), 11F11 (Secondary) |
| url | https://arxiv.org/abs/2507.14118 |