Thirty-two Goldbach Variations
By Jonathan Michael Borwein, David M. Bradley. 2005
71 citations recorded by the source corpus.
We give thirty-two diverse proofs of a small mathematical gem — the fundamental Euler sum identity 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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/aa999ef975887bd184fffd992e0ff276d0f07300
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- The evaluation of Tornheim double sums. Part 2 (2005, background): “T (1, 1, 6) = [2, 0, 0, 0, 0, 0] , T (2, 1, 5) = [2, 1, 0, 0, 0, 0] , T (2, 2, 4) = [4, 2, 0, 0, 0, 0] , T (3, 1, 4) = [2, 1, 1, 0, 0, 0] , T (3, 2, 3) = [6, 3, 1, 0, 0, 0] , T (3, 3, 2) = [12, 6, 2, 0, 0, 0] , T (4, 1, 3) = [2, 1, 1, 1, 0, 0] , T (4, 2, 2) = [8, 4, 2, 1, 0, 0] , T (4, 3, 1) = [20, ”
- Nonlinear Euler sums (2014, background): “The most fundamental one is the following [Borwein and Bradley 2006]:”