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 348 · Answer 1 · 2026-04-28 08:42:15

348

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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 28 Apr 2026 - 8:42

score 342 · Answer 2 · 2026-05-10 13:27:18

342

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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 10 May 2026 - 13:27

score 579 · Answer 3 · 2026-05-10 14:28:23

579

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Liouville function and perfect square 2.

Published on 10 May 2026 - 14:28

score 143 · Answer 4 · 2026-05-10 14:27:21

143

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

Published on 10 May 2026 - 14:27

score 369 · Answer 5 · 2026-05-10 14:29:10

369

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

Published on 10 May 2026 - 14:29

score 774 · Answer 6 · 2026-05-10 14:31:32

774

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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 10 May 2026 - 14:31

score 82 · Answer 7 · 2026-05-06 08:01:10

82

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prove you have found all such functions

Published on 06 May 2026 - 8:01

score 84 · Answer 8 · 2026-05-03 05:35:10

84

Views

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

Published on 03 May 2026 - 5:35

score 230 · Answer 9 · 2026-05-10 14:29:01

230

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

Published on 10 May 2026 - 14:29

score 809 · Answer 10 · 2026-05-10 14:29:10

809

Views

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

Published on 10 May 2026 - 14:29

score 100 · Answer 11 · 2026-05-10 14:29:02

100

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Why do fractal-like patterns appear in this sequence?

Published on 10 May 2026 - 14:29

score 121 · Answer 12 · 2026-05-10 14:32:19

121

Views

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

Published on 10 May 2026 - 14:32

score 117 · Answer 13 · 2026-05-10 14:27:22

117

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Liouville Lambda Function and Riemann Hypothesis

Published on 10 May 2026 - 14:27

score 739 · Answer 14 · 2026-05-10 14:29:09

739

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

Published on 10 May 2026 - 14:29

score 560 · Answer 15 · 2026-05-10 14:32:06

560

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

Published on 10 May 2026 - 14:32

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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