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Tagged with liouville-function elementary-number-theory
5 questions
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Inclusion-exclusion formula for the Liouville Lambda function.
The Riemann hypothesis is equivalent to:
$$\lim_{n\to \infty } \, \frac{\sum\limits_{k=1}^n \lambda (k)}{n^{\frac{1}{2}+\epsilon}}=0$$
according to "The Riemann Hypothesis: A Resource for the ...
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Is $\lambda (n/d)$ is also multiplicative?
Let $\lambda$ denote the Liouville $\lambda $- function. We know that $\lambda$ is multiplicative if we define it for integers $n$.
It is defined here:
https://math.stackexchange.com/posts/3245975/...
- 3,127
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Liouville function and perfect square 2.
As a proof of the second part of part(b) of this question :
Liouville function and perfect square
I have the solution given below:
But I can not see how this solution explains the case when $n =5 \...
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Generalisation of the Liouville function as irreducible representations for $(\mathbb{N},\cdot)$?
These are only going to be a soft questions. And I thought this question is also a case for MO, so I have posted a duplicate there (Does that comply with the etiquette here? In case not I am sorry.)
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Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$
Inverting $\displaystyle\sum_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$ into $\displaystyle\sum_{d|n} \lambda(n/d) 2^{\omega(d)}=1$ ,where $n \geq1$, by using Mobius Inversion Formula.
I'm able to solve ...
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