## Preventing Exceptions to Robins InEquality

Por • 19 ago, 2013 • Sección: Crítica

Thomas Schwabhäuser

Abstract: For sufficiently large n Ramanujan gave a sufficient condition for the truth Robin’s InEquality $X(n):=\frac{\sigma(n)}{n\ln\ln n}<e^{\gamma}$ (RIE). The largest known violation of RIE is $n_8=5040$. In this paper Robin’s multipliers are split into logarithmic terms $\mathcal{L}$ and relative divisor sums $\mathcal{G}$. A violation of RIE above $n_{8}$ is proposed to imply oscillations that cause $\mathcal{G}$ to exceed $\mathcal{L}$. To this aim Alaoglu and Erd\H{o}s’s conjecture for the CA numbers algorithm is used and the paper’s key points are in section 4.2

arXiv:1308.3678v1 [math.NT]