Arithmetic properties of the Ramanujan function

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dc.creatorLuca, Florian
dc.creatorShparlinski, Igor E
dc.date2006-07-24
dc.date.accessioned2026-07-07T07:20:51Z
dc.date.available2026-07-07T07:20:51Z
dc.descriptionWe study some arithmetic properties of the Ramanujan function $τ(n)$, such as the largest prime divisor $P(τ(n))$ and the number of distinct prime divisors $ω(τ(n))$ of $τ(n)$ for various sequences of $n$. In particular, we show that \hbox{$P(τ(n)) \geq (\log n)^{33/31 + o(1)}$} for infinitely many $n$, and \begin{equation*} P(τ(p)τ(p^2)τ(p^3)) > (1+o(1))\frac{\log\log p\log\log\log p} {\log\log\log\log p} \end{equation*} for every prime $p$ with \hbox{$τ(p)\neq 0$}.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0607591
dc.identifierhttp://arxiv.org/abs/math/0607591
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115096
dc.subjectNumber Theory
dc.titleArithmetic properties of the Ramanujan function
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