Question

What's about the convergence of $\sum_{n=1}^\infty\frac{\mu(n)\pi_2(n)}{n^2}$, on assumption of the Twin Prime Conjecture?

score 45 · Answer 1 · 2016-12-08 14:30:35

45

Views

What's about the convergence of $\sum_{n=1}^\infty\frac{\mu(n)\pi_2(n)}{n^2}$, on assumption of the Twin Prime Conjecture?

Published on 08 Dec 2016 - 14:30

score 63 · Answer 2 · 2016-12-13 10:43:57

63

Views

On the convergence of $\sum_{n=1}^\infty\log \left(\frac{\mu(n)}{\sqrt{n}}+1-\frac{1}{4n^2}\right)$, where $\mu(n)$ is the Möbius function

Published on 13 Dec 2016 - 10:43

score 408 · Answer 3 · 2016-12-15 11:10:38

408

Views

On $\sum_{n=1}^\infty\frac{\mu\left(\lfloor \sqrt{n} \rfloor\right)-\mu\left(\lceil \sqrt{n} \rceil\right)}{n}$ and the Möbius function

Published on 15 Dec 2016 - 11:10

score 66 · Answer 4 · 2016-12-15 17:39:40

66

Views

$\sum_{n=1}^7\frac{\mu(n)}{n^s}$ has a zero with $\Re s>1$, where $\mu(n)$ is the Möbius function

Published on 15 Dec 2016 - 17:39

score 87 · Answer 5 · 2016-12-15 20:46:34

87

Views

On the asymptotic behaviour of $\sum_{k=1}^N\mu(k)\sum_{n=-k}^k f(n)$, where $f$ is a Schwartz function and $\mu(n)$ the Möbius function

Published on 15 Dec 2016 - 20:46

score 129 · Answer 6 · 2016-12-17 00:49:19

129

Views

Alternative proof for this formula?

Published on 17 Dec 2016 - 0:49

score 703 · Answer 7 · 2026-03-25 15:21:41

703

Views

Dirichlet series associated to squared Möbius

Published on 25 Mar 2026 - 15:21

score 213 · Answer 8 · 2016-12-18 13:55:36

213

Views

On the convergence of a series involving the Riemann Zeta function

Published on 18 Dec 2016 - 13:55

score 111 · Answer 9 · 2016-12-29 20:50:09

111

Views

Provide me a numerical calculation to check my final identity involving powers of the inverse sine and Lambert series for the Möbius function

Published on 29 Dec 2016 - 20:50

score 472 · Answer 10 · 2026-03-26 01:14:30

472

Views

Is this Dirichlet "$\eta$ version" of the inverse relationship between $\zeta(s)$ and the Möbius function correct?

Published on 26 Mar 2026 - 1:14

score 760 · Answer 11 · 2017-01-10 22:19:44

760

Views

The density of square-free integers satisfying a congruence relation

Published on 10 Jan 2017 - 22:19

score 129 · Answer 12 · 2017-01-11 15:23:25

129

Views

A definition of the functional $f\to\sum_{n=1}^\infty\mu(n)f \left( \frac{1}{n} \right) $, involving good functions $f$ and the Möbius function

Published on 11 Jan 2017 - 15:23

score 136 · Answer 13 · 2017-01-11 18:36:00

136

Views

A telescoping series with the Möbius function. Does a closed form exist?

Published on 11 Jan 2017 - 18:36

score 104 · Answer 14 · 2017-01-14 15:30:10

104

Views

From the definition of $f(s)=\sum_{n=1}^\infty\frac{\mu(n)-\mu(n+1)}{n^s}$ to an identity $1-f(s)=S(s)+T(s)$

Published on 14 Jan 2017 - 15:30

score 2k · Answer 15 · 2026-03-25 14:46:56

2k

Views

Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

Published on 25 Mar 2026 - 14:46

List Question

What's about the convergence of $\sum_{n=1}^\infty\frac{\mu(n)\pi_2(n)}{n^2}$, on assumption of the Twin Prime Conjecture?

On the convergence of $\sum_{n=1}^\infty\log \left(\frac{\mu(n)}{\sqrt{n}}+1-\frac{1}{4n^2}\right)$, where $\mu(n)$ is the Möbius function

On $\sum_{n=1}^\infty\frac{\mu\left(\lfloor \sqrt{n} \rfloor\right)-\mu\left(\lceil \sqrt{n} \rceil\right)}{n}$ and the Möbius function

$\sum_{n=1}^7\frac{\mu(n)}{n^s}$ has a zero with $\Re s>1$, where $\mu(n)$ is the Möbius function

On the asymptotic behaviour of $\sum_{k=1}^N\mu(k)\sum_{n=-k}^k f(n)$, where $f$ is a Schwartz function and $\mu(n)$ the Möbius function

Alternative proof for this formula?

Dirichlet series associated to squared Möbius

On the convergence of a series involving the Riemann Zeta function

Provide me a numerical calculation to check my final identity involving powers of the inverse sine and Lambert series for the Möbius function

Is this Dirichlet "$\eta$ version" of the inverse relationship between $\zeta(s)$ and the Möbius function correct?

The density of square-free integers satisfying a congruence relation

A definition of the functional $f\to\sum_{n=1}^\infty\mu(n)f \left( \frac{1}{n} \right) $, involving good functions $f$ and the Möbius function

A telescoping series with the Möbius function. Does a closed form exist?

From the definition of $f(s)=\sum_{n=1}^\infty\frac{\mu(n)-\mu(n+1)}{n^s}$ to an identity $1-f(s)=S(s)+T(s)$

Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

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