5 papers
New Application of the large-Nc expansion : comparison of the Gottfried and Adler sum rules
D. J. Broadhurst, A. L. Kataev, C. J. Maxwell
The Adler sum rule for deep inelastic neutrino scattering measures the isospin of the nucleus, and is hence exact. In contrast the Gottfried sum rule for charged lepton scattering…
Central Binomial Sums, Multiple Clausen Values and Zeta Values
J. M. Borwein, D. J. Broadhurst, J. Kamnitzer
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums). The study of non-alte…
Dimensionally continued multi-loop gauge theory
D. J. Broadhurst
A dimensionally continued background-field method makes the rationality of the 4-loop quenched QED beta function far more reasonable than had previously appeared. After 33 years of…
Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links
J. M. Borwein, D. J. Broadhurst
We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers and giving $a/b vol(M)=(-D)^{3/2}/(2π)^{2n…
Evaluations of k-fold Euler/Zagier sums: a compendium of results for arbitrary k
J. M. Borwein, D. M. Bradley, D. J. Broadhurst
Euler sums (also called Zagier sums) occur within the context of knot theory and quantum field theory. There are various conjectures related to these sums whose incompletion is a s…