• On exponential sums involving the Ramanujan function

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      https://www.ias.ac.in/article/fulltext/pmsc/097/01-03/0157-0166

    • 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

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