A case study for \(\zeta (4)\)

DOI10.1007/978-3-030-84304-5_17zbMath1499.11271arXiv2004.08158OpenAlexW3214470680MaRDI QIDQ2097085

Yanyan Li

Publication date: 11 November 2022

Full work available at URL: https://arxiv.org/abs/2004.08158

zbMATH Keywords

rational approximationsdifference rings

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) (zeta (s)) and (L(s, chi)) (11M06)

Related Items (1)

The SAGEX review on scattering amplitudes Chapter 4: Multi-loop Feynman integrals

Uses Software

• SIGMA
• EvaluateMultiSums
• RhoSum

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Calculating three loop ladder and \(V\)-topologies for massive operator matrix elements by computer algebra
• A difference ring theory for symbolic summation
• Well-poised hypergeometric series for Diophantine problems of zeta values
• Parameterized telescoping proves algebraic independence of sums
• Apéry's double sum is plain sailing indeed
• A refined difference field theory for symbolic summation
• Differential Galois theory of linear difference equations
• A hypergeometric problem
• A holonomic systems approach to special functions identities
• The method of creative telescoping
• Hypergeometric solutions of linear recurrences with polynomial coefficients
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Solving difference equations in finite terms
• Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects
• Refined holonomic summation algorithms in particle physics
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• An extension of Zeilberger's fast algorithm to general holonomic functions
• Two definite integrals that are definitely (and surprisingly!) equal
• Plane partitions. VI: Stembridge's TSPP theorem
• A new Sigma approach to multi-summation
• Symbolic summation assists combinatorics
• Fast Algorithms for Refined Parameterized Telescoping in Difference Fields
• On an Integral Identity
• Hypergéométrie et fonction zêta de Riemann
• Summation in Finite Terms
• Hypergeometric rational approximations to ζ(4)
• Creative Telescoping for Holonomic Functions
• Simplifying Multiple Sums in Difference Fields

This page was built for publication: A case study for \(\zeta (4)\)