Thirty-two Goldbach Variations

Details Thirty-two Goldbach Variations Thirty-two Goldbach Variations

2005-02-01

arxiv.org/abs/math/0502034v2

International Journal of Number Theory, Vol. 2, No. 1 (2006), pp. 65--103. MR2217795 (2007e:11109)

Mathematics

Number Theory

v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and

Scientific paper

10.1142/S1793042106000383

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). 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.

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