# Thirty-two Goldbach Variations

Borwein, Jonathan M. and Bradley, David M. (2006) Thirty-two Goldbach Variations. Int. J. Number Theory, 2 (1). pp. 65-103.

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## Abstract

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

Item Type: Article pubdom TRUE Multiple harmonic series, multiple zeta values, Euler sums, Euler-Zagier sums 11-xx Number theory > 11Mxx Zeta and $L$-functions: analytic theory40-xx Sequences, series, summability > 40Bxx Multiple sequences and series UNSPECIFIED Users 1 not found. 12 Sep 2005 12 Jan 2015 13:28 https://docserver.carma.newcastle.edu.au/id/eprint/301

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