On page 532 of the book analytic number theory by Iwaniec and Kowalski, the following notation is used:
$C^{~\infty}$ and $\tau(n,\chi)$.
Could anyone tell me what these represent? (the former is definitely not functions!)
Thanks!
2026-03-28 14:53:27.1774709607
Iwaniec Kowalski Notation
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$c|C^{\infty}$ just means that $c|C^k$ for large $k$.
$\tau(n,\chi)$ is a twisted divisor function $\sum_{d|n} \chi(d)$.