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 48 · Answer 1 · 2026-04-13 20:23:46

48

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 13 Apr 2026 - 20:23

score 66 · Answer 2 · 2026-04-16 07:15:14

66

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 16 Apr 2026 - 7:15

score 411 · Answer 3 · 2026-04-14 20:57:13

411

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 14 Apr 2026 - 20:57

score 69 · Answer 4 · 2026-04-14 23:26:26

69

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 14 Apr 2026 - 23:26

score 90 · Answer 5 · 2026-04-15 08:13:57

90

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 Apr 2026 - 8:13

score 131 · Answer 6 · 2026-04-08 16:59:33

131

Views

Alternative proof for this formula?

Published on 08 Apr 2026 - 16:59

score 705 · Answer 7 · 2026-04-15 08:53:21

705

Views

Dirichlet series associated to squared Möbius

Published on 15 Apr 2026 - 8:53

score 216 · Answer 8 · 2026-04-13 16:35:21

216

Views

On the convergence of a series involving the Riemann Zeta function

Published on 13 Apr 2026 - 16:35

score 114 · Answer 9 · 2026-04-10 05:29:37

114

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 10 Apr 2026 - 5:29

score 476 · Answer 10 · 2026-04-16 16:56:30

476

Views

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

Published on 16 Apr 2026 - 16:56

score 763 · Answer 11 · 2026-04-14 04:32:15

763

Views

The density of square-free integers satisfying a congruence relation

Published on 14 Apr 2026 - 4:32

score 132 · Answer 12 · 2026-04-15 12:51:50

132

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 15 Apr 2026 - 12:51

score 139 · Answer 13 · 2026-04-14 11:49:14

139

Views

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

Published on 14 Apr 2026 - 11:49

score 107 · Answer 14 · 2026-04-16 12:25:49

107

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 16 Apr 2026 - 12:25

score 2k · Answer 15 · 2026-05-11 01:11:08

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 11 May 2026 - 1:11

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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