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# Questions tagged [multiplicative-number-theory]

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### Math software / language for analytic / multiplicative number theory

What software/languages are the most used to do computations in analytic / multiplicative number theory? I use Python, Maple, etc., but each time I want to compute expressions like, for $n$ with an ...
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I'm interesting to know more about multiplicative property of integer functions then I'd like to ask this humble question: Question: Is it possible to find all integer functions which satisfy $f(m!+... 6 votes 1 answer 301 views ### A question about$(0,1]$-valued multiplicative functions Suppose$f:\mathbb{N}\to [0,1]$is a multiplicative function (i.e.$f(nm)=f(n)f(m)$whenever$m$and$n$are coprime). Suppose$f$has non-zero mean, which means$$\lim_{N\to\infty}\frac{1}{N} \sum_{... 10 votes 0 answers 206 views ### The multiplicative group generated by shifted primes 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$\... 1 vote
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### All all hypo-multiplicative functions linear combinations of quasi-multiplicative functions?

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 quasi-...
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### Least prime in an arithmetic progression and the Selberg sieve

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 $k$ ...