English

Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}

High Energy Physics - Phenomenology 2026-02-11 v1 Numerical Analysis High Energy Physics - Theory Mathematical Physics math.MP Numerical Analysis

Abstract

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 qq-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 qq-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.

Keywords

Cite

@article{arxiv.2602.09956,
  title  = {Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}},
  author = {Claude Duhr and Florian Lorkowski and Robin Marzucca and Sofia Mauc and Stefan Weinzierl},
  journal= {arXiv preprint arXiv:2602.09956},
  year   = {2026}
}

Comments

29 pages, 3 figures, discussed code to be released in GiNaC

R2 v1 2026-07-01T10:29:59.997Z