• On exponential sums involving the Ramanujan function

    • Fulltext


        Click here to view fulltext PDF

      Permanent link:

    • Keywords


      Exponential sums; Ramanujan τ function

    • Abstract


      Let τ(n) be the arithmetical function of Ramanujan, α any real number, and x≥2. The uniform estimate$$\mathop \Sigma \limits_{n \leqslant x} \tau (n)e(n\alpha ) \ll x^6 \log x$$ is a classical result of J R Wilton. It is well known that the best possible bound would be ≪x6. The validity of this hypothesis is proved.

    • Author Affiliations


      M Jutila1

      1. Department of Mathematics, University of Turku, Turku - SF-20500, Finland
    • Dates

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.