- Hi Everyone,

Does anyone have code for computing more accurate Riemann

approximations to pi(x) by utilizing additional zeros of the Riemann

Zeta function? I think Bays and Hudson did something like that using

100,000 zeros to find a sign change for Li(x) - pi(x) near 1.39822 *

10^316. I am also looking for pi(x) code for the latest algorithms.

Thanks,

David Baugh - Ask Andrey Kulsha, who knows a thing or two about that crossover:

http://listserv.nodak.edu/scripts/wa.exe?A2=ind0111&L=nmbrthry&P=R61 - Hello!

David Baugh wrote:

> Does anyone have code for computing more accurate Riemann

The code used by me is too specific and too slow, but I can provide you an algorithm.

> approximations to pi(x) by utilizing additional zeros of the Riemann

> Zeta function?

> I think Bays and Hudson did something like that using

Yes, there are some pretty plots in their paper (Math Comp., 2000) which I'm looking for.

> 100,000 zeros to find a sign change for Li(x) - pi(x) near 1.39822 *

> 10^316.

> I am also looking for pi(x) code for the latest algorithms.

Try to ask Xavier Gourdon, his code seem to be very fast.

* * * * *

David Broadhurst wrote:

> Ask Andrey Kulsha, who knows a thing or two about that crossover:

The result given here isn't proven, it requires both RH and SH to be true. All I can add is that the constant 0.09238... = 2*(gamma-log(4*pi)+2), where gamma = 0.5772...

> http://listserv.nodak.edu/scripts/wa.exe?A2=ind0111&L=nmbrthry&P=R61

Best,

Andrey

[Non-text portions of this message have been removed] > > 0.09238... = 2*(gamma-log(4*pi)+2),

H. Davenport, "Multiplicative Number Theory" (2nd ed.), Berlin, 1980, pp. 80-83.

> Excellent. Is this written up?

Best,

Andrey

[Non-text portions of this message have been removed]