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Tagged with liouville-function reference-request
4 questions
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Liouville Lambda Function and Riemann Hypothesis
What is the exact statement involving the Liouville Lambda function, which is equivalent to Riemann Hypothesis, and true iff RH is true? Can anyone cite the sources for it and/or outline its proof in ...
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3
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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?
Let $\lambda(n)$, for integers $n\geq 1$, be the Liouville lambda function, defined by $\lambda(n)=(-1)^{\Omega(n)}$ where $\Omega(n)$ is the number of prime factors of $n$, counted with multiplicity. ...
user243301
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About a more efficient way of evaluating $L(n):=\sum_{k=1}^n\lambda(k)$, where $\lambda(n)$ is the Liouville function, than this definition of $L(n)$
Let for integers $n\geq 1$ the Möbius function $\mu(n)$, and $\lambda(n)$ the Liouville function (see the definition in this Wikipedia). We consider also the corresponding summary functions $$M(n)=\...
user243301
3
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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 ...
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