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arXiv · 1202.0729

Small values of the Euler function and the Riemann hypothesis

Jean-Louis Nicolas
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Abstract

Let $\vfi$ be Euler's function, $\ga$ be Euler's constant and $N_k$ be the product of the first $k$ primes. In this article, we consider the function $c(n) =(n/\vfi(n)-e^\ga\log\log n)\sqrt{\log n}$. Under Riemann's hypothesis, it is proved that $c(N_k)$ is bounded and explicit bounds are given while, if Riemann's hypothesis fails, $c(N_k)$ is not bounded above or below.

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Jean-Louis Nicolas. 2012-04-05. Small values of the Euler function and the Riemann hypothesis. https://arxiv.org/abs/1202.0729

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