All Questions

I am looking for an upper-bound of the Euler's totient function $\varphi$ which would be equivalent to the Riemann hypothesis (RH). There is the following Nicolas' criterion about primorial numbers $...

In Guy Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. 63 (1984), 187–213 (pdf) we find the following result: If the Riemann hypothesis is true ...

Let $M(x)$ denote the Mertens function ($M(x)=\sum_{i=1}^{x}\mu(i)$ where $\mu(i)$ is the Möbius function) and let $\Lambda(i)$ denote the Mangoldt function ($\Lambda(i)$ equals $\log(p)$ if $i=p^{m}$ ...

Let $\Lambda(n)$ denote the von Mangoldt function: $\Lambda(n)=\log p$ when $n=p^e$ is a prime power ($e\ge 1$) and $\Lambda(n)=0$ otherwise. and $\lambda(n)$ be Liouville Function, , I'm interested ...

Jeffrey Lagarias proved, unconditionally, that: $$ \sigma(n)<H_n+2\exp(H_n)\log(H_n)\qquad n>1 $$ This was posed as a problem in: J. C. Lagarias, Problem 10949: A generous bound for divisor ...