Question

How to invert this relationship (Möbius function involved)?

score 112 · Answer 1 · 2026-03-26 01:27:29

112

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How to invert this relationship (Möbius function involved)?

Published on 26 Mar 2026 - 1:27

score 225 · Answer 2 · 2026-04-15 10:55:51

225

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On calculations for $\prod_{k=2}^\infty \left( 1+\frac{\mu(k)}{k^3} x\right)$, where $\mu(n)$ is the Möbius function

Published on 15 Apr 2026 - 10:55

score 108 · Answer 3 · 2026-04-17 02:12:04

108

Views

What's about $\sum_{n=1}^\infty\frac{\mu(n)}{n}f(X^{\frac{1}{n}})$, where $\mu(n)$ is the Möbius function?

Published on 17 Apr 2026 - 2:12

score 991 · Answer 4 · 2026-04-16 01:57:50

991

Views

Number of squarefree integers $n \le x$ with $\omega(n)$ even

Published on 16 Apr 2026 - 1:57

score 88 · Answer 5 · 2026-03-25 23:42:16

88

Views

An interesting connection between the Möbius function and the parity of the number of sublattices of index $n$ in generic $3$-dimensional lattice

Published on 25 Mar 2026 - 23:42

score 93 · Answer 6 · 2026-04-17 02:35:22

93

Views

Can you provide us an asymptotic for this series involving Mertens functions?

Published on 17 Apr 2026 - 2:35

score 147 · Answer 7 · 2026-04-14 03:12:50

147

Views

Riemann Hypothesis and $\sum\limits_{k\leq n}\left(\frac{\mu(k)}{k}\right)^2$

Published on 14 Apr 2026 - 3:12

score 59 · Answer 8 · 2026-04-14 18:47:37

59

Views

On the convergence of $\sum_{k=1}^\infty\frac{\mu(k)\{\frac{1}{ky}\}}{k}$ where $\mu(n)$ is the Möbius function and $0< y\leq 1$ is fixed

Published on 14 Apr 2026 - 18:47

score 140 · Answer 9 · 2026-04-11 13:46:24

140

Views

Möbius function equation

Published on 11 Apr 2026 - 13:46

score 4.8k · Answer 10 · 2026-04-13 14:35:34

4.8k

Views

The Möbius function is the sum of the primitive $n$th roots of unity.

Published on 13 Apr 2026 - 14:35

score 524 · Answer 11 · 2026-04-14 06:45:30

524

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Is This Proof Valid? - $\sum_{k=1}^{n}\mu(k!)=1$ for $n \geq 3$

Published on 14 Apr 2026 - 6:45

score 295 · Answer 12 · 2026-04-11 22:21:11

295

Views

A simple exercise on integration by residues and an application of Jordan's lemma

Published on 11 Apr 2026 - 22:21

score 1.2k · Answer 13 · 2026-05-11 01:13:01

1.2k

Views

Provide us a detailed explanation to calculate the Mellin transform of a cosine function, and get the closed form of a related sum

Published on 11 May 2026 - 1:13

score 107 · Answer 14 · 2026-04-16 16:04:46

107

Views

Calculate $\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^T\frac{\zeta(\frac{3}{2}+it)}{\zeta(\frac{3}{2}-it)}dt$ as $\sum_{n=1}^\infty\frac{\mu(n)}{n^3}$

Published on 16 Apr 2026 - 16:04

score 84 · Answer 15 · 2026-04-10 02:41:00

84

Views

On calculations involving the Möbius function and the integral representation for the Riemann Zeta function for $\Re s>1$

Published on 10 Apr 2026 - 2:41

List Question

How to invert this relationship (Möbius function involved)?

On calculations for $\prod_{k=2}^\infty \left( 1+\frac{\mu(k)}{k^3} x\right)$, where $\mu(n)$ is the Möbius function

What's about $\sum_{n=1}^\infty\frac{\mu(n)}{n}f(X^{\frac{1}{n}})$, where $\mu(n)$ is the Möbius function?

Number of squarefree integers $n \le x$ with $\omega(n)$ even

An interesting connection between the Möbius function and the parity of the number of sublattices of index $n$ in generic $3$-dimensional lattice

Can you provide us an asymptotic for this series involving Mertens functions?

Riemann Hypothesis and $\sum\limits_{k\leq n}\left(\frac{\mu(k)}{k}\right)^2$

On the convergence of $\sum_{k=1}^\infty\frac{\mu(k)\{\frac{1}{ky}\}}{k}$ where $\mu(n)$ is the Möbius function and $0< y\leq 1$ is fixed

Möbius function equation

The Möbius function is the sum of the primitive $n$th roots of unity.

Is This Proof Valid? - $\sum_{k=1}^{n}\mu(k!)=1$ for $n \geq 3$

A simple exercise on integration by residues and an application of Jordan's lemma

Provide us a detailed explanation to calculate the Mellin transform of a cosine function, and get the closed form of a related sum

Calculate $\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^T\frac{\zeta(\frac{3}{2}+it)}{\zeta(\frac{3}{2}-it)}dt$ as $\sum_{n=1}^\infty\frac{\mu(n)}{n^3}$

On calculations involving the Möbius function and the integral representation for the Riemann Zeta function for $\Re s>1$

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