Kyle Pratt

Half-isolated zeros and zero-density estimates

We discuss a new zero-detecting method which is sensitive to the vertical distribution of zeros of the zeta function. This allows us to show that there are few ‘half-isolated’ zeros. If we assume that the zeros of the zeta function are restricted to finitely many vertical lines, then we can improve upon classical zero-density results of Ingham and Huxley. This is joint work with James Maynard and Roger Heath-Brown.