THIRTY-TWO GOLDBACH VARIATIONS

2005/02/28 by Jonathan M. Borwein, JONATHAN M. BORWEIN, David M. Bradley +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #math.NT #msc:11M41

paper · pdf · doi:10.1142/s1793042106000383

published as International Journal of Number Theory, Vol. 2, No. 1 (2006), pp. 65--103. MR2217795 (2007e:11109) · v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title changed

arxiv created 2005/11/03 · openalex publication_date 2006/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give thirty-two diverse proofs of a small mathematical gem — the fundamental Euler sum identity [Formula: see text] We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.

Citations

• A q‐analog of Euler′s decomposition formula forthe double zeta function
• Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth
• Duality for finite multiple harmonic q-series
• Multiple q-zeta values
• The Algebra and Combinatorics of Shuffles andMultiple Zeta Values

Cited by

• On Eulerian log-gamma integrals and Tornheim–Witten zeta functions