Question

How to invert this relationship (Möbius function involved)?

score 111 · Answer 1 · 2020-07-10 19:58:23

111

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How to invert this relationship (Möbius function involved)?

Published on 10 Jul 2020 - 19:58

score 222 · Answer 2 · 2016-07-12 21:18:27

222

Views

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 12 Jul 2016 - 21:18

score 104 · Answer 3 · 2016-07-14 19:38:20

104

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 14 Jul 2016 - 19:38

score 988 · Answer 4 · 2016-07-15 20:12:16

988

Views

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

Published on 15 Jul 2016 - 20:12

score 87 · Answer 5 · 2016-07-18 02:27:13

87

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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 18 Jul 2016 - 2:27

score 88 · Answer 6 · 2016-07-19 12:38:04

88

Views

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

Published on 19 Jul 2016 - 12:38

score 144 · Answer 7 · 2016-07-28 07:40:44

144

Views

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

Published on 28 Jul 2016 - 7:40

score 56 · Answer 8 · 2016-08-07 21:36:38

56

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 07 Aug 2016 - 21:36

score 137 · Answer 9 · 2016-08-10 20:16:37

137

Views

Möbius function equation

Published on 10 Aug 2016 - 20:16

score 4.8k · Answer 10 · 2016-08-14 22:34:48

4.8k

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

Published on 14 Aug 2016 - 22:34

score 521 · Answer 11 · 2016-08-25 12:15:38

521

Views

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

Published on 25 Aug 2016 - 12:15

score 292 · Answer 12 · 2016-08-30 07:31:05

292

Views

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

Published on 30 Aug 2016 - 7:31

score 1.1k · Answer 13 · 2026-03-25 13:58:12

1.1k

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 25 Mar 2026 - 13:58

score 105 · Answer 14 · 2026-03-25 19:07:07

105

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 25 Mar 2026 - 19:07

score 81 · Answer 15 · 2016-09-19 14:45:49

81

Views

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

Published on 19 Sep 2016 - 14:45

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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