A still sharper region where π(x) - li(x) is positive

Yannick Saouter, Timothy Trudgian, Patrick Demichel

    Research output: Contribution to journalArticlepeer-review

    17 Citations (Scopus)

    Abstract

    We consider the least number x for which a change of sign of π(x)-li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new smaller upper bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.

    Original languageEnglish
    Pages (from-to)2433-2446
    Number of pages14
    JournalMathematics of Computation
    Volume84
    Issue number295
    DOIs
    Publication statusPublished - 2015

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