Abstract:
We consider the following two problems. We are given the values of several initial derivatives of the Riemann zeta function calculated at some (unknown to us) point $a$.
• How could we calculate an approximate value of the function itself at the same point a without prior finding this number?
• How could we find an approximate value of $a$ itself?
We suggest several algorithms for answering these questions and demonstrate their accuracy on a few numerical examples. The algorithms reveal some new properties of the zeta function.
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