• M Jutila

Articles written in Proceedings – Mathematical Sciences

• On exponential sums involving the Ramanujan function

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.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019