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Extended Fractal Fits to Riemann Zeros | | Paul B. Slater
; | | Date: |
21 May 2007 | | Subject: | Mathematical Physics (math-ph) | | Abstract: | We extend to the first 300 Riemann zeros, the form of analysis reported by us
in arXiv:math-ph/0606005, in which the largest study had involved the first 75
zeros. Again, we model the nonsmooth fluctuating part of the Wu-Sprung
potential, which reproduces the Riemann zeros, by the alternating-sign sine
series fractal of Berry and Lewis A(x,g). Setting the fractal dimension equal
to 3/2. we estimate the frequency parameter (g), plus an overall scaling
parameter (s) introduced. We search for that pair of parameters (g,s) which
minimizes the least-squares fit of the lowest 300 eigenvalues -- obtained by
solving the one-dimensional stationary (non-fractal) Schrodinger equation with
the trial potential (smooth plus nonsmooth parts) -- to the first 300 Riemann
zeros. We randomly sample values within the rectangle 0 < s < 3, 0 < g < 25.
The fits obtained are compared to those gotten by using simply the smooth part
of the Wu-Sprung potential without any fractal supplementation. Some limited
improvement is again found. There are two (primary and secondary) quite
distinct subdomains, in which the values giving improvements in fit are
concentrated. | | Source: | arXiv, arxiv.0705.3031 | | Services: | Forum | Review | PDF | Favorites | |
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