I'm reading a survey article by Andrew Granville on analytic number theory.
On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot below.
Since it's not defined in the paper, I'm assuming it must be standard notation.
From the context, I'm assuming it means something like "as compared to", or "with reference to", but that's just a guess.
Can anyone identify the symbol, even better explain what it means and/or provide a reference? Is there a name to speak the symbol?
Thanks in advance.
Best Answer
It can mean different things depending on the context. For instance, in Graham, Knuth, and Patashnik's Concrete Mathematics it's defined to mean the same thing as "Big $\Theta$" (see p. 448), as in
$$ f \asymp g \iff \exists\, C,D>0 : C|g| \leq |f| \leq D|g|, $$
but I read a paper recently where it was instead defined to mean the same thing as $\sim$ (as defined here).