ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 26 Jul 2013 13:42:03 +0200Hadamard product for the Riemann zeta functionhttps://ask.sagemath.org/question/10390/hadamard-product-for-the-riemann-zeta-function/What is the best way to compute numerically with Sage the product
over the first n nontrivial zeros of the Riemann zeta function?
<pre><code>p(s,n) = product((1-s/rho(k))*exp(s/rho(k)) for k in (1..n))</code></pre>
where zeta(rho(k)) == 0 and Im(rho(k)) != 0.
Wikipedia advises: "To ensure convergence the product should be
taken over 'matching pairs' of zeroes, i.e. the factors for a
pair of zeroes of the form rho(k) and 1-rho(k) should be combined."
[Hadamard product on MathWorld](http://mathworld.wolfram.com/HadamardProduct.html)
petropolisFri, 26 Jul 2013 13:42:03 +0200https://ask.sagemath.org/question/10390/