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Hilbert’s Inequality and Witten’s Zeta-function

Borwein, Jonathan M. (2008) Hilbert’s Inequality and Witten’s Zeta-function. American Math Monthly, 115 (2). pp. 125-137.

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    Abstract

    We explore a variety of pleasing connections between analysis, number theory and operator theory, while revisiting a number of beautiful inequalities originating with Hilbert, Hardy and others. We shall first establish the aforementioned Hilbert inequality and then apply it to various multiple zeta values. In consequence we obtain the norm of the classical Hilbert matrix, while illustrating the interplay of numerical and symbolic computation with classical mathematics.

    Item Type: Article
    Additional Information: pubdom TRUE
    Subjects: 26-xx Real functions > 26Dxx Inequalities
    11-xx Number theory
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 01 Jan 2006
    Last Modified: 11 Jan 2015 18:03
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/309

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