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On some trigonometric and exponential lattice sums

Borwein, David and Borwein, Jonathan M. (1994) On some trigonometric and exponential lattice sums. Journal of Mathematical Analysis and Applications., 188 . pp. 209-218. ISSN 0022-247X

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    Abstract

    Certain two-dimensional trigonometric lattice series, the ordinary convergence of which involves unresolved questions of a deep and delicate number-theoretic nature, are shown to be summable by a special Abelian method and their Abelian sums are obtained. This is done by first evaluating an absolutely convergent exponential lattice series and then analytically extending its sum.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 14 Jan 2015 10:17
    Last Modified: 14 Jan 2015 10:17
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1542

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