• M Jutila

      Articles written in Proceedings – Mathematical Sciences

    • On exponential sums involving the Ramanujan function

      M Jutila

      More Details Abstract Fulltext PDF

      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.

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