Question

On calculations concerning the exact formula for the Mertens function, and the identity that relates Möbius and Mertens functions

score 250 · Answer 1 · 2026-04-16 05:14:51

250

Views

On calculations concerning the exact formula for the Mertens function, and the identity that relates Möbius and Mertens functions

Published on 16 Apr 2026 - 5:14

score 200 · Answer 2 · 2026-04-24 01:23:39

200

Views

Kummer's transformation applied to a series involving the Möbius function: were rights my deductions and how get an idea of the improvement?

Published on 24 Apr 2026 - 1:23

score 105 · Answer 3 · 2026-04-16 18:18:22

105

Views

What's about the generating function for the Mertens function?

Published on 16 Apr 2026 - 18:18

score 86 · Answer 4 · 2026-05-11 04:18:22

86

Views

Why does $N$ divide $\sum_{d|N} p^{md} \mu\bigg(\frac{N}{d}\bigg)$?

Published on 11 May 2026 - 4:18

score 163 · Answer 5 · 2026-04-11 11:52:21

163

Views

A congruence involving odd perfect numbers and the Möbius function

Published on 11 Apr 2026 - 11:52

score 206 · Answer 6 · 2026-04-15 19:37:33

206

Views

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

Published on 15 Apr 2026 - 19:37

score 184 · Answer 7 · 2026-04-11 17:17:48

184

Views

The definition of the complex function $\sum_{n=1}^{\infty}\frac{\mu(n)}{n}z^n$ on the open disk, where $\mu(n)$ is the Möbius function

Published on 11 Apr 2026 - 17:17

score 103 · Answer 8 · 2026-05-11 03:00:28

103

Views

On a doubt about a simple exercise concerning Nachbin resummation

Published on 11 May 2026 - 3:00

score 73 · Answer 9 · 2026-04-14 22:56:57

73

Views

Prove that $\sum_{n=1}^\infty\mu(n)z^{\mu(n)n}$ has an essential singularity at the origin, where $\mu(n)$ is the Möbius function

Published on 14 Apr 2026 - 22:56

score 163 · Answer 10 · 2026-04-13 15:05:11

163

Views

Can you combine integration by parts and the infinite product that satisfies the exponential and Möbius function?

Published on 13 Apr 2026 - 15:05

score 167 · Answer 11 · 2026-04-14 21:17:47

167

Views

More about integration by parts and the Möbius function: the product $\prod_{n=1}^\infty\left(1+x^n\right)^{\mu(n)/n}$

Published on 14 Apr 2026 - 21:17

score 134 · Answer 12 · 2026-04-11 06:28:12

134

Views

An infinite product involving the Möbius function, and $\sum_{k=1}^N\frac{\mu(k)}{k!}$

Published on 11 Apr 2026 - 6:28

score 67 · Answer 13 · 2026-04-16 00:16:32

67

Views

On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

Published on 16 Apr 2026 - 0:16

score 2.4k · Answer 14 · 2026-05-10 22:32:00

2.4k

Views

Dirichlet Convolution of the Mobius Function with Itself

Published on 10 May 2026 - 22:32

score 59 · Answer 15 · 2026-04-09 12:36:46

59

Views

How can I compute the Möbius function?

Published on 09 Apr 2026 - 12:36

List Question

On calculations concerning the exact formula for the Mertens function, and the identity that relates Möbius and Mertens functions

Kummer's transformation applied to a series involving the Möbius function: were rights my deductions and how get an idea of the improvement?

What's about the generating function for the Mertens function?

Why does $N$ divide $\sum_{d|N} p^{md} \mu\bigg(\frac{N}{d}\bigg)$?

A congruence involving odd perfect numbers and the Möbius function

On the representation $\Gamma(z)=\sum_{n=2}^\infty \int_0^\infty a(n)e^{-e^{nx}}e^{nzx}dx$, for arithmetic functions $a(n)$ and $\Re z>0$

The definition of the complex function $\sum_{n=1}^{\infty}\frac{\mu(n)}{n}z^n$ on the open disk, where $\mu(n)$ is the Möbius function

On a doubt about a simple exercise concerning Nachbin resummation

Prove that $\sum_{n=1}^\infty\mu(n)z^{\mu(n)n}$ has an essential singularity at the origin, where $\mu(n)$ is the Möbius function

Can you combine integration by parts and the infinite product that satisfies the exponential and Möbius function?

More about integration by parts and the Möbius function: the product $\prod_{n=1}^\infty\left(1+x^n\right)^{\mu(n)/n}$

An infinite product involving the Möbius function, and $\sum_{k=1}^N\frac{\mu(k)}{k!}$

On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

Dirichlet Convolution of the Mobius Function with Itself

How can I compute the Möbius function?

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