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About | The Mobius function Blog
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The Mobius function Blog. Just another WordPress.com weblog. This blog aims to be about the Möbius function described here: http:/ mathworld.wolfram.com/MoebiusFunction.html. But tends to focus much on matrix inversion of triangular matrices. Are the amplitudes o…. On Fourier transform of exponenti…. On Logarithmic square root w…. On First differences of most nega…. Nick on The inverse of a triangular ma…. On The inverse of a triangular ma…. The Mobius function Blog. Build a website with WordPress.com.
Magic series and Magic constants | The Mobius function Blog
https://mobiusfunction.wordpress.com/2013/05/16/magic-series-and-magic-constants
The Mobius function Blog. Just another WordPress.com weblog. Riemann zeta function on the critical line as a Fourier transform of exponential sawtooth function plus minus one. Arne Bergstroms paper →. Magic series and Magic constants. May 16, 2013. Craig Knecht sent me an email explaining magic series and magic constants. The following program lists magic series that add up to certain constants using the TableForm command in Mathematica:. Program for reordering of integer partitions start*). Create a fre...
First differences of most negative eigenvalues of a symmetric matrix. | The Mobius function Blog
https://mobiusfunction.wordpress.com/2011/11/04/first-differences-of-most-negative-eigenvalues-of-symmetric-matrix
The Mobius function Blog. Just another WordPress.com weblog. Pi raised to fraction of second and third Riemann zeta zeros – seven repeating decimals. Rough plot of the von Mangoldt function →. First differences of most negative eigenvalues of a symmetric matrix. November 4, 2011. Clear[a, t, n, k, i, j]. T[n, k] =. If[n = k, -Sum[t[n - i, k], {i, 1, k - 1}], -Sum[. A = Range[1, nn]*0;. B = Range[1, nn]*0;. M = Table[Table[t[n, k], {k, 1, j}], {n, 1, j}];. A[ j] = Eigenvalues[m],. The Mobius function Blog.
The inverse of a triangular matrix using forward substitution | The Mobius function Blog
https://mobiusfunction.wordpress.com/2010/12/21/the-inverse-of-a-triangular-matrix-using-forward-substitution
The Mobius function Blog. Just another WordPress.com weblog. Mobius function “recursion”. Mobius matrix →. The inverse of a triangular matrix using forward substitution. December 21, 2010. This post is about how to invert a lower triangular matrix. Which is the matrix inverse of another. We take the definition of matrix inversion as a starting point:. Is the matrix multiplication of. Is the identity matrix, kind of the equivalent of the number 1 of the natural numbers 1,2,3… but as a matrix. Thanks, it h...
The Mobius function Blog | Just another WordPress.com weblog | Page 2
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The Mobius function Blog. Just another WordPress.com weblog. Newer posts →. January 12, 2013. A visual interpretation of Riemann zeta zeros via the Fourier transform. December 18, 2012. Scale = 1000000;. Xres = .001;. Limit = 3000;. X = Exp[Range[0, Log[scale], xres] ;. A = FourierDCT[(SawtoothWave[x])*x (-1/2)];. B = -FourierDST[(SawtoothWave[x] – 1)*x (-1/2)];. ListLinePlot[( SawtoothWave[x])*x (-1/2) [ 1; limit] ]*). Gs = ListLinePlot[-( SawtoothWave[x] – 1)*x (-1/2) [ 1 ; limit] ,. December 17, 2012.
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The Mobius function Blog | Just another WordPress.com weblog
The Mobius function Blog. Just another WordPress.com weblog. Interesting iterative formula that fails to converge to Riemann zeta zeros for c close to 1. June 24, 2017. 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 n=0 text{ then } frac{n cdot mu (n)}{k s} text{ else } 0$. Where $ mu(n)$ is the Möbius function. So thereby there is/exist...
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