On solving a curious inequality of ramanujan

Adrian W. Dudek*, David J. Platt

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    Ramanujan proved that the inequality [equation presented] holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp (9658). Furthermore, we solve the inequality completely on the Riemann hypothesis and show that x = 38 358 837 682 is the largest integer counterexample.

    Original languageEnglish
    Pages (from-to)289-294
    Number of pages6
    JournalExperimental Mathematics
    Volume24
    Issue number3
    DOIs
    Publication statusPublished - 3 Jul 2015

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