Algebraic independence of sequences generated by (cyclotomic) harmonic sums

DOI10.1007/s00026-018-0381-5zbMath1444.11153arXiv1510.03692OpenAlexW2963325921WikidataQ129937618 ScholiaQ129937618MaRDI QIDQ1653307

Carsten Schneider, Jakob Ablinger

Publication date: 3 August 2018

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.03692

zbMATH Keywords

algebraic independencequasi-shuffle algebradifference ringscyclotomic harmonic sumsring of sequences

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Algebraic independence; Gel'fond's method (11J85) Special sequences (11K31) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (8)

Analytic computing methods for precision calculations in quantum field theory ⋮ Hypergeometric structures in Feynman integrals ⋮ Refined telescoping algorithms in RΠΣ -extensions to reduce the degrees of the denominators✱ ⋮ Automated solution of first order factorizable systems of differential equations in one variable ⋮ The two-mass contribution to the three-loop gluonic operator matrix element \(A_{g g, Q}^{(3)}\) ⋮ The absent-minded passengers problem: a motivating challenge solved by computer algebra ⋮ Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation ⋮ The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Uses Software

• HarmonicSums
• EvaluateMultiSums

Cites Work

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