I am asking for references about the following problem. In particular, it is still open? If not, what is the state of the art result? Problem 1. Let $\Gamma$ be the multiplicative subgroup of ...
A function is called quasi-multiplicative by many authors if $f(m)f(n)=f(1)f(mn)$, a slight generalization of multiplicativity. (Basically a multiplicative function times a constant is a ...
My question concerns a technical step in the proof of Linnik's theorem on the least prime in an arithmetic progression, as presented in Chapter 18 of Iwaniec-Kowalski: Analytic number theory. The ...
Carlitz showed necessary and sufficient conditions for an arithmetic function to be a linear combination of two multiplicative functions. He mentions the possibility of generalizing to $k$ ...
Is there an explicit formula for the number of fourth powers mod n? Finch & Sebah  give theorems, partially folklore, for squares and cubes mod n, but I don't know of a similar formula for ...