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Tagged with liouville-function mobius-function
3 questions
2
votes
1
answer
389
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Questions on Convergence of Explicit Formulas for $f(x)=\sum\limits_{n=1}^x a(n)$ where $a(n)\in\{\left|\mu(n)\right|,\mu(n),\phi(n),\lambda(n)\}$
This question is a follow-on to my earlier question at the following link.
What is the explicit formula for $\Phi(x)=\sum\limits_{n=1}^x\phi(n)$?
This question pertains to the explicit formulas for ...
- 8,141
3
votes
0
answers
595
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What is the origin of this Riemann Hypothesis equivalent involving the Liouville function?
Peter Borwein (in his 2006 book The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, p. 6) provides an equivalence between the Riemann Hypothesis and this conjecture involving ...
- 31
1
vote
1
answer
843
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Prove $\lambda(n)=\sum_{d^2|n}\mu(n/d)^2$ and $\mu^2(n)=\sum_{d^2|n}\mu(d)$
$\lambda(n)$= $\sum_{d^2|n}$ $\mu(n/d)^2$
and $\mu^2(n)$= $\sum_{d^2|n}$ $\mu(d)$
Having a little bit of trouble here.Can I use the fact that $\sum_{d|n}\lambda(n)$ is a characteristic function for ...
- 760