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http://pastebin.com/kk9fHAaC

Let be 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 →

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 →

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: Mathematica 8: (*program for reordering of integer partitions start*) TableForm[ … Continue reading →

Riemann zeta function on the critical line as a Fourier transform of exponential sawtooth function plus minus one The code does not work when copy pasted in this blogging platform, so here is a link to Pastebin with some working … Continue reading →

Mathematica 8: 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]], PlotStyle -> RGBColor[1, 0, 1]]; gsine = ListLinePlot[ … Continue reading →