Taking the fractional part of a sum with an integer

Question

In Hildebrand and Tenenbaum's Integers without large prime factors, I've come across the equation $$\Psi(x,y)=x\rho(u)\bigg\{1+O\bigg(\frac{log(u+1)}{log\ y}\bigg)\bigg\}$$ My understanding of the braces here is that they take the fractional part of a number e.g. $\{3.7\}=0.7$ and so wouldn't $\{1+k\}=\{k\}$? I assume something about the big-Oh part gives this meaning, but I don't understand why adding one has any effect here.

Answer 1

As it happens, no, they just mean large brackets by the curly braces. This is confusing, but happens with some regularity in older analytic number theory texts (see e.g. Apostol's classic texts; they're riddled with places in which $\{\dots\}$ means fractional part or just grouping, depending on (to the beginner very vague) context).