Upper bounds for prime k-tuples of size log N and oscillations

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    Abstract

    We prove the estimate Ek ≪ N/exp((1/4 + o(1)) log N log log log N/log log N), for the number Ek (N) of k-tuples (n + a 1, . . ., n + ak) of primes not exceeding N, for k of size c1 log N and N sufficiently large. A bound of this strength was previously known in the special case n - 2i (1 ≦ i <log n/log 2) only, (Vaughan, 1973). For general ai this is an improvement upon the work of Hofmann and Wolke (1996). The number of prime tuples of this size has considerable oscillations, when varying the prime pattern.

    Original languageEnglish
    Pages (from-to)33-39
    Number of pages7
    JournalArchiv der Mathematik
    Volume82
    Issue number1
    DOIs
    Publication statusPublished - Jan 2004

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    Upper bounds for prime k-tuples of size log N and oscillations. / Elsholtz, Christian.

    In: Archiv der Mathematik, Vol. 82, No. 1, 01.2004, p. 33-39.

    Research output: Contribution to journalArticleResearchpeer-review

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