Short Talks by Postdoctoral Members

In this talk, we present some new results on the joint distribution function of the argument and the norm of the Riemann zeta function on the 1-line (the edge of the critical strip). Our strategy is to introduce a probabilistic random model for these values. One consequence of our work is the fact that almost all values of \zeta(1+it) with large norm are concentrated near the positive real axis. We also show that the arguments (when suitably normalized) of large values of \zeta(1+it) are normally distributed with mean 0. Similar results are also given for the family L(1,\chi) (as \chi varies over non-principal characters modulo a large prime.