The Distribution of Values of the Riemann Zeta Function and Dirichlet L-functions on the 1-Line

 SHORT TALKS BY POSTDOCTORAL MEMBERS Topic: The Distribution of Values of the Riemann Zeta Function and Dirichlet L-functions on the 1-Line Speaker: Youness Lamzouri Affiliation: Member, School of Mathematics Date: Tuesday, September 29 Time/Room: 2:00pm - 3:00pm/S-101

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.