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Computing the first $n$ values of the Liouville function in linear time

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#number-theory #prime-numbers #computational-complexity #sieve-theory #liouville-function
478
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Liouville's Theorem Applications

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#complex-analysis #liouville-function
76
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How quickly can this function be computed?

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#number-theory #computational-complexity #liouville-function
85
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What about $x\frac{f'(x)}{f(x)}=-\frac{1}{2}\left(\vartheta_3(x)-1\right)$, where $\vartheta_3(x)$ is Jacobi theta function?

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#ordinary-differential-equations #infinite-product #theta-functions #liouville-function
176
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Minimal value of summatory function of completely multiplicative functions taking values -1 and 1

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#number-theory #prime-numbers #analytic-number-theory #multiplicative-function #liouville-function
69
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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 $L(n)$

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#number-theory #reference-request #recursive-algorithms #arithmetic-functions #liouville-function
141
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Is it possible to deduce that the limit $\lim_{x\to-\infty}\sum_{n=1}^\infty\lambda(n)\frac{x^n}{\Gamma(n)}$ is finite?

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#real-analysis #sequences-and-series #convergence-divergence #gamma-function #liouville-function
117
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Generalisation of the Liouville function as irreducible representations for $(\mathbb{N},\cdot)$?

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#group-theory #elementary-number-theory #soft-question #liouville-function
160
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$\sum_{d\mid n}\lambda(d)\sigma(d)=n\lambda(n)\sum_{d^2\mid n}\frac{1}{d^2}$ Solution

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#number-theory #arithmetic #liouville-function
399
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The Dirichlet series for the Liouville function related to the Riemann zeta function

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#riemann-zeta #dirichlet-series #liouville-function
128
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Inclusion-exclusion formula for the Liouville Lambda function.

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#sequences-and-series #elementary-number-theory #inclusion-exclusion #liouville-function
193
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Dirichlet transform of $e^{(2 \pi i / 3) \Omega(n)}$

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#number-theory #riemann-zeta #dirichlet-series #liouville-function
192
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Values of the Liouville function

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#number-theory #prime-numbers #prime-factorization #liouville-function
134
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Turán proof that constant sign of Liouville function implies RH

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#analytic-number-theory #riemann-zeta #dirichlet-series #riemann-hypothesis #liouville-function

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