## Interesting iterative formula that fails to converge to Riemann zeta zeros for c close to 1

Let the matrix $A$ be the lower triangular matrix defined as: $$A=\text{If } n \bmod k=0 \text{ then } \frac{1}{n^c} \text{ else } 0$$ and let the matrix $B$ be the upper triangular matrix defined as: B=\text{If } k \bmod … Continue reading

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## Polynomial root find algorithm

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## Dirichlet series for a symmetric matrix

Let be the Möbius function

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## Train of thought leading from the zeta function to the Möbius function

(*start Mathematica 8*) (*Start with Riemann zeta:*) Zeta[s] (*Take the logarithm:*) Log[Zeta[s]] (*Take the derivative:*) D[Log[Zeta[s]], s] Clear[s, c] (*Generalize it:*) Limit[Zeta[c] – Zeta[s]*Zeta[c]/Zeta[s + c – 1], c -> 1] (*See that Zeta[s]*Zeta[c]/Zeta[s+c-1] is the Dirichlet generating \ function … Continue reading

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## The Möbius function times n

1, -2, -3, 0, -5, 6, -7, 0, 0, 10, -11, 0, -13, 14, 15, 0, -17, 0, -19, 0, 21, 22, -23, 0, 0, 26, 0, 0, -29, -30, -31, 0, 33, 34, 35, 0, -37, 38, 39, 0, … Continue reading

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## Arne Bergstroms paper 26 6 2013

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## Arne Bergstroms paper

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