Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908826241859584 |
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| author | Duhr, Claude Lorkowski, Florian Marzucca, Robin Mauc, Sofia Weinzierl, Stefan |
| author_facet | Duhr, Claude Lorkowski, Florian Marzucca, Robin Mauc, Sofia Weinzierl, Stefan |
| contents | We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of elliptic multiple polylogarithms. Its coefficients are expressed in terms of ordinary multiple polylogarithms, which can be evaluated efficiently using existing libraries. In a series of preparation steps the elliptic polylogarithms are mapped into a region where the $q$-series converges rapidly. We also present an implementation of our algorithm into the \texttt{GiNaC} framework. This release constitutes the first public package capable of evaluating elliptic multiple polylogarithms to high precision and for arbitrary values of the arguments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC} Duhr, Claude Lorkowski, Florian Marzucca, Robin Mauc, Sofia Weinzierl, Stefan High Energy Physics - Phenomenology Numerical Analysis High Energy Physics - Theory Mathematical Physics We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of elliptic multiple polylogarithms. Its coefficients are expressed in terms of ordinary multiple polylogarithms, which can be evaluated efficiently using existing libraries. In a series of preparation steps the elliptic polylogarithms are mapped into a region where the $q$-series converges rapidly. We also present an implementation of our algorithm into the \texttt{GiNaC} framework. This release constitutes the first public package capable of evaluating elliptic multiple polylogarithms to high precision and for arbitrary values of the arguments. |
| title | Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC} |
| topic | High Energy Physics - Phenomenology Numerical Analysis High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.09956 |