Corpus ID: 235755269

The numerical evaluation of the Riesz function

  title={The numerical evaluation of the Riesz function},
  author={Richard B. Paris},
The behaviour of the generalised Riesz function defined by Sm,p(x) = ∞ ∑ k=0 (−)x k!ζ(mk + p) (m ≥ 1, p ≥ 1) is considered for large positive values of x. A numerical scheme is given to compute this function which enables the visualisation of its asymptotic form. The two cases m = 2, p = 1 and m = p = 2 (introduced respectively by Hardy and Littlewood in 1918 and Riesz in 1915) are examined in detail. It is found on numerical evidence that these functions appear to exhibit the x and x decay… Expand

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