Question

What is the closed-form of $\sum_{n=1}^\infty\lambda(n)\log\cosh\frac{1}{n}$, where $\lambda(n)$ is the Liouville function?

score 344 · Answer 1 · 2026-03-24 23:46:11

344

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What is the closed-form of $\sum_{n=1}^\infty\lambda(n)\log\cosh\frac{1}{n}$, where $\lambda(n)$ is the Liouville function?

Published on 24 Mar 2026 - 23:46

score 335 · Answer 2 · 2026-03-25 01:18:38

335

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Questions on Convergence of Explicit Formulas for $f(x)=\sum\limits_{n=1}^x a(n)$ where $a(n)\in\{\left|\mu(n)\right|,\mu(n),\phi(n),\lambda(n)\}$

Published on 25 Mar 2026 - 1:18

score 572 · Answer 3 · 2026-03-25 01:15:05

572

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Liouville function and perfect square 2.

Published on 25 Mar 2026 - 1:15

score 136 · Answer 4 · 2026-03-25 01:13:10

136

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Is $\lambda (n/d)$ is also multiplicative?

Published on 25 Mar 2026 - 1:13

score 357 · Answer 5 · 2026-03-25 01:21:55

357

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Question on Divisor Sum over the Liouville Function $\lambda(d)=(-1)^{\omega(d)}$

Published on 25 Mar 2026 - 1:21

score 763 · Answer 6 · 2026-03-25 07:48:28

763

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Prove $\lambda(n)=\sum_{d^2|n}\mu(n/d)^2$ and $\mu^2(n)=\sum_{d^2|n}\mu(d)$

Published on 25 Mar 2026 - 7:48

score 75 · Answer 7 · 2026-03-22 10:44:42

75

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prove you have found all such functions

Published on 22 Mar 2026 - 10:44

score 79 · Answer 8 · 2020-03-17 09:59:46

79

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Is a bounde entire function of exponential type constant on a any compact?

Published on 17 Mar 2020 - 9:59

score 224 · Answer 9 · 2026-03-25 11:14:10

224

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There are infinitely many positive integers $n$ such that $\lambda(n) = \lambda(n+1)=\lambda(n+2) = +1$;

Published on 25 Mar 2026 - 11:14

score 804 · Answer 10 · 2026-03-25 01:21:55

804

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Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$

Published on 25 Mar 2026 - 1:21

score 89 · Answer 11 · 2026-03-25 01:15:29

89

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Why do fractal-like patterns appear in this sequence?

Published on 25 Mar 2026 - 1:15

score 113 · Answer 12 · 2026-02-28 14:29:56

113

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I dont understand the last step. I’m trying to understand how equation 10 follows, especially the last delta equation

Published on 28 Feb 2026 - 14:29

score 111 · Answer 13 · 2026-03-22 17:48:54

111

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Liouville Lambda Function and Riemann Hypothesis

Published on 22 Mar 2026 - 17:48

score 733 · Answer 14 · 2026-02-28 14:28:35

733

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$\sum_{n=1}^N\lambda(n)[N/n]=[\sqrt{N}]$ Identity involving Liouville Lambda function

Published on 28 Feb 2026 - 14:28

score 552 · Answer 15 · 2026-02-28 14:26:36

552

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What is the origin of this Riemann Hypothesis equivalent involving the Liouville function?

Published on 28 Feb 2026 - 14:26

List Question

What is the closed-form of $\sum_{n=1}^\infty\lambda(n)\log\cosh\frac{1}{n}$, where $\lambda(n)$ is the Liouville function?

Questions on Convergence of Explicit Formulas for $f(x)=\sum\limits_{n=1}^x a(n)$ where $a(n)\in\{\left|\mu(n)\right|,\mu(n),\phi(n),\lambda(n)\}$

Liouville function and perfect square 2.

Is $\lambda (n/d)$ is also multiplicative?

Question on Divisor Sum over the Liouville Function $\lambda(d)=(-1)^{\omega(d)}$

Prove $\lambda(n)=\sum_{d^2|n}\mu(n/d)^2$ and $\mu^2(n)=\sum_{d^2|n}\mu(d)$

prove you have found all such functions

Is a bounde entire function of exponential type constant on a any compact?

There are infinitely many positive integers $n$ such that $\lambda(n) = \lambda(n+1)=\lambda(n+2) = +1$;

Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$

Why do fractal-like patterns appear in this sequence?

I dont understand the last step. I’m trying to understand how equation 10 follows, especially the last delta equation

Liouville Lambda Function and Riemann Hypothesis

$\sum_{n=1}^N\lambda(n)[N/n]=[\sqrt{N}]$ Identity involving Liouville Lambda function

What is the origin of this Riemann Hypothesis equivalent involving the Liouville function?

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