Negative values of the Riemann zeta function on the critical line
  We investigate the intersections of the curve $\mathbb{R}\ni t\mapsto \zeta({1\over 2}+it)$ with the real axis. We show unconditionally that the zeta-function takes arbitrarily large positive and negative values on the critical line. 
Justas Kalpokas, Maxim A. Korolev, J\"orn Steuding
math.NT