Concerning an upper bound for closely spaced zeroes of the Riemann zeta-function on the critical line.
by
Timothy Trudgian
Mathematical Institute, University of Oxford

Estimates concerning the propensity of zeroes of multiplicity greater than one have been investigated by Titchmarsh, Selberg and more recently Fujii and Korolev. Using Gram's Law - the method first used for searching for zeroes computationally (which this year celebrates its centenary) - it is possible to give a partial extension of these results. Included are estimates on the frequency of failures of Gram's Law along with an upper bound for the number of zeroes occurring between successive Gram points.

Date received: June 19, 2008