Zeta FunctionsSeptember 18  22, 2006, Moscow, RussiaLaboratoire J.V. Poncelet 

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

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