Half-isolated zeros and zero-density estimates by James Maynard

We introduce 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, and allows us to
improve the classical zero density result to
N(σ, T) T 24(1−σ)/11+o(1)

if we assume that the zeros of the zeta function are restricted to finitely
many vertical lines (and so gives new results about primes in short
intervals under this assumption). This is joint work with Kyle Pratt.