4 papers
Searching symbolically for Apery-like formulae for values of the Riemann zeta function
Jonathan M. Borwein, David M. Bradley
We discuss some aspects of the search for identities using computer algebra and symbolic methods. The focus is on so-called Apery-like formulae for special values of the Riemann Ze…
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…
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…