Florian Luca: Small values of the Ramanujan $\tau$-function, 467-470

Abstract:

Here, we show that if $\tau(n)$ is the Ramanujan $\tau$-function, then there exists a function $f(n)$ tending to infinity such that $\vert\tau(n)\vert/n^{11/2}<(\log n)^{-f(n)}$ holds for an infinite sequence of positive integers $n$.

Key Words: The Ramanujan $\tau$-function.

2020 Mathematics Subject Classification: Primary 11F11; Secondary 11F30, 11F41.

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