Polylogarithmic functions with prescribed branching locus and linear relations between them

2024/07/17 by Roman N. Lee, Lee, Roman N.
Mathematics · #Advanced Mathematical Identities #Analytic and geometric function theory #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2407.12503

openalex publication_date 2024/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of finding the set of classical polylogarithmic functions Li_n with branching locus determined by the solution of p₁⋅ p₂⋅ … ⋅ p_n=0, where p₁,…, p_n are irreducible polynomials of several variables. We present an algorithm of constructing a complete set of possible arguments of Li_n functions. The corresponding Mathematica code is included as ancillary file. Using this algorithm and the symbol map, we provide some examples of polylogarithmic identities.

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