List questions from analytic-number-theory

Published on 10 Apr 2026 - 2:26

195

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Show that $\sum\limits_{n\in \mathbb N} \frac{2^{\omega(n)}}{n^s}=\frac{\zeta^2(s)}{\zeta(2s)}$.

Published on 15 Apr 2026 - 4:16

38

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Generalization of Distribution of Smooth Integers to Algebraic Number Fields

Published on 14 Apr 2026 - 22:56

37

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Where can I learn to develop Effective Versions of Asymptotic Theorems?

Published on 15 Apr 2026 - 11:07

94

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Big Oh notation and quantitative integral test

Published on 11 Apr 2026 - 20:34

433

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Smoothing in analytic number theory

Published on 10 Apr 2026 - 4:11

672

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How soon can we represent a number as the sum of two primes?

Published on 10 Apr 2026 - 8:51

43

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Smoothing function details in analytic number theory paper

Published on 09 Apr 2026 - 15:21

236

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If $p$ is the largest prime less than $2n$, what is the probability that $2n-p$ is a prime?

Published on 15 Apr 2026 - 9:10

229

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On an approximation to Goldbach's conjecture

Published on 26 Mar 2026 - 8:14

994

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Sum of reciprocals of primes: easy proof that $\sum_{p\leq x} \frac{1}{p} < C\log\log x$ for some constant $C$?

Published on 16 Apr 2026 - 7:25

88

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Can a certain subset of $\mathbb{N}$ be written as an intersection of subsets with natural densities?

Published on 13 Apr 2026 - 10:37

88

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Does this “Euclidean” sum of reciprocals of primes converge?

Published on 12 Apr 2026 - 22:10

102

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Show that $\sum\limits_{n\leq x} \varphi(n)=\frac{1}{2}\sum\limits_{n\leq x}\mu(n)[\frac{x}{n}]^2+\frac{1}{2}$.

Published on 15 Apr 2026 - 22:07

56

Views

$\zeta'(s)\ll (\log t)^2$ using Cauchy's formula, proof verification

Published on 12 Apr 2026 - 4:56

List Question

Iwaniec & Kowalski distribution of additive functions

Show that $\sum\limits_{n\in \mathbb N} \frac{2^{\omega(n)}}{n^s}=\frac{\zeta^2(s)}{\zeta(2s)}$.

Generalization of Distribution of Smooth Integers to Algebraic Number Fields

Where can I learn to develop Effective Versions of Asymptotic Theorems?

Big Oh notation and quantitative integral test

Smoothing in analytic number theory

How soon can we represent a number as the sum of two primes?

Smoothing function details in analytic number theory paper

If $p$ is the largest prime less than $2n$, what is the probability that $2n-p$ is a prime?

On an approximation to Goldbach's conjecture

Sum of reciprocals of primes: easy proof that $\sum_{p\leq x} \frac{1}{p} < C\log\log x$ for some constant $C$?

Can a certain subset of $\mathbb{N}$ be written as an intersection of subsets with natural densities?

Does this “Euclidean” sum of reciprocals of primes converge?

Show that $\sum\limits_{n\leq x} \varphi(n)=\frac{1}{2}\sum\limits_{n\leq x}\mu(n)[\frac{x}{n}]^2+\frac{1}{2}$.

$\zeta'(s)\ll (\log t)^2$ using Cauchy's formula, proof verification

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