https://www.cmi.ac.in/~shreejit/Zeta-Function.pdf
"Our goal in this note is to discuss the behaviour of $\zeta(s)$ in the critical strip $0\leq\sigma\leq1$. More precisely, we want to inspect how $\zeta(s)$ varies with $t$, the imaginary part of $s$, in an infinite vertical strip in this critical region. One of the most intriguing hypothesis in this direction is the Lindelof hypothesis. It states that for any $e\gt0$, $\zeta(0.5+it)\ll t^e$, where $\ll$ denotes order" so is that the same as saying $\zeta(0.5+it)\in O(t^e)$ ?
Vinogradov used "<<" to mean what Landau (and almost all following writers) writes as $O(...)$