# Author Archives: Mats Granvik

## 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

## 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

## Magic series and Magic constants

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