Laboratoire J.-V. Poncelet
Steklov Mathematical Institute, Russia
Zeroes of the Riemann xi-function and its derivatives lying on the critical line.
The Riemann xi-function is an entire function of order one and its zeroes coincide with non-trivial zeroes of the Riemann zeta-function which lie in the critical strip. The Riemann hypothesis asserts that all zeroes of the Riemann xi-function lie on the critical line. This remains neither proved nor disproved yet.
It was observed that zeroes of all derivatives of the xi-function also lie in the critical strip. Moreover, if the Riemann hypothesis is fulfilled, then all zeroes of derivatives of the Riemann xi-function lie on the critical line.
The talk would be devoted to survey of milestone results concerning zeroes of the Riemann xi-function and its derivatives. A brief insight into applied methods will be communicated as well.
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