The asymptotics of a new exponential sum

Richard B. Paris

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)


    The absolutely convergent exponential sum [formula missing] is studied for m→+∞ and fixed p when the parameter θ is allowed to become large such that θ/m remains finite. This situation corresponds, in general, to the trace in the complex plane of the partial sums of Sp(θ;m) consisting of a multiple spiral structure. Numerical results are presented to illustrate the accuracy of the expansion.
    Original languageEnglish
    Pages (from-to)314-325
    Number of pages12
    JournalJournal of Computational and Applied Mathematics
    Issue number1
    Publication statusPublished - 1 Jan 2009


    • Exponential sums
    • Gauss sum
    • Asymptotics
    • Curlicues


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