• On exponential sums involving the Ramanujan function

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019