Thirty-two Goldbach Variations
Number Theory
2007-06-13 v2
Abstract
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.
Cite
@article{arxiv.math/0502034,
title = {Thirty-two Goldbach Variations},
author = {Jonathan M. Borwein and David M. Bradley},
journal= {arXiv preprint arXiv:math/0502034},
year = {2007}
}
Comments
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