# Questions tagged [multiplicative-number-theory]

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### Results using a certain kind of identity

Recently, I've been reading about asymptotics for smooth numbers as well as smooth numbers in arithmetic progressions. One of the ideas I find especially pleasing among some of these results is the ...
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### Numbers made up of primes from a given set

Take a set $\mathcal P$ of primes and denote by $\langle \mathcal P\rangle$ the set of all natural numbers composed of primes from $\mathcal P$. If $\sum _{p\in \mathcal P}\frac {1}{p}$ converges ...
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### Function multiplicativity

Is this a multiplicative function? $\displaystyle \sum_{a=1 \atop (a,q)=1}^{q}e^{-2\pi i\frac{a}{q}c_q(da)F}=T(q)$,where $d,F\in \mathbb{N}$ and $c_q(da)$ - Ramanujan's sum https://en.m.wikipedia.org/...
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### Recovering basic information about perfect numbers from a Dirichlet series

The following question is inspired mostly by this question, answer and the comment by Wojowu there A naive approach to understanding odd perfect numbers is to make a Dirichlet series where the $n$th ...
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### Well-known estimate for $L(s,\chi)$ for $\sigma=\text{Re}s\geq 1/2$

This is a very short question. Let $s=\sigma+it$ be a complex number with $\sigma \geq 1/2$. In the paper 'Jutila, Matti. "On the Mean Value of $L(1/2, \chi)$ FW Real Characters." Analysis 1.2 (...
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### Questions about a certain set of primes

Let $A$ be a set of prime numbers, generated by the following procedure. Let $A_0 = \{2\}$. Let $A_n$ be generated by setting $x_n = (\prod_{p_i \in A_{n-1}}p_i) + 1$, and adding all the prime factors ...
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### Uniformity in Wirsing's Mean Value Theorems

In two important papers of Wirsing, namely "Das asymptotische Verhalten von Summen über multiplikative Funktionen" (1961) and its follow up (1967), several results on mean values of multiplicative ...
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