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zeraoulia rafik
zeraoulia rafik
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In searching through the Riemann Nachlass in Gottingen (including those folders not listed as connected with \zeta(s)) $\zeta(s)) $ there is no evidence -- at least that has been saved -- that Riemann computed anything more than the first few zeros (I think up to ordinate about 80).
The method he used was the expansion that is now called the Riemann-Siegel formula. I did not see any use, e.g., of an approach based on Euler-Maclaurin. The limited accuracy Riemann obtained reflects that of the error term in the R-S formula.

In searching through the Riemann Nachlass in Gottingen (including those folders not listed as connected with \zeta(s)) there is no evidence -- at least that has been saved -- that Riemann computed anything more than the first few zeros (I think up to ordinate about 80).
The method he used was the expansion that is now called the Riemann-Siegel formula. I did not see any use, e.g., of an approach based on Euler-Maclaurin. The limited accuracy Riemann obtained reflects that of the error term in the R-S formula.

In searching through the Riemann Nachlass in Gottingen (including those folders not listed as connected with $\zeta(s)) $ there is no evidence -- at least that has been saved -- that Riemann computed anything more than the first few zeros (I think up to ordinate about 80).
The method he used was the expansion that is now called the Riemann-Siegel formula. I did not see any use, e.g., of an approach based on Euler-Maclaurin. The limited accuracy Riemann obtained reflects that of the error term in the R-S formula.

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Dennis Hejhal
Dennis Hejhal
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In searching through the Riemann Nachlass in Gottingen (including those folders not listed as connected with \zeta(s)) there is no evidence -- at least that has been saved -- that Riemann computed anything more than the first few zeros (I think up to ordinate about 80).
The method he used was the expansion that is now called the Riemann-Siegel formula. I did not see any use, e.g., of an approach based on Euler-Maclaurin. The limited accuracy Riemann obtained reflects that of the error term in the R-S formula.