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

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.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0003-DE41-A Version Permalink: https://hdl.handle.net/21.11116/0000-0003-DE42-9
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Garcia-Luca_On The Difference In Values Of The Euler Totient_2018.pdf (Publisher version), 327KB
 
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 Creators:
Garcia, Stephan Ramon, Author
Luca, Florian1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 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 $50\%$.

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Language(s): eng - English
 Dates: 2018
 Publication Status: Issued
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 Rev. Type: -
 Identifiers: arXiv: 1706.00392
URI: http://arxiv.org/abs/1706.00392
DOI: 10.1007/978-3-319-92777-0_4
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Title: Irregularities in the distribution of prime numbers : from the era of Helmut Maier’s matrix method and beyond
Source Genre: Book
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Publ. Info: Cham : Springer
Pages: XI, 217 S. Volume / Issue: - Sequence Number: - Start / End Page: 69 - 96 Identifier: ISBN: 978-3-319-92776-3
DOI: 10.1007/978-3-319-92777-0