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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
    Additional Information: pubdom TRUE
    Uncontrolled Keywords: Multiple harmonic series, multiple zeta values, Euler sums, Euler-Zagier sums
    Subjects: 11-xx Number theory > 11Mxx Zeta and $L$-functions: analytic theory
    40-xx Sequences, series, summability > 40Bxx Multiple sequences and series
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 12 Sep 2005
    Last Modified: 12 Jan 2015 13:28
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/301

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