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Book Chapter

On the difference in values of the Euler totient function near prime arguments

MPS-Authors
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Luca,  Florian
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

arXiv:1706.00392.pdf
(Preprint), 268KB

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Citation

Garcia, S. R., & Luca, F. (2018). On the difference in values of the Euler totient function near prime arguments. In Irregularities in the distribution of prime numbers: from the era of Helmut Maier’s matrix method and beyond (pp. 69-96). Cham: Springer.


Cite as: http://hdl.handle.net/21.11116/0000-0003-DE41-A
Abstract
We prove unconditionally that for each $\ell \geq 1$, the difference $\phi(p-\ell) - \phi(p+\ell)$ is positive for $50\%$ of odd primes $p$ and negative for $50\%$.