Abstract: The distribution of the zeros of the derivative of the Riemann zeta-function has a fascinating connection to the zeros of ζ(s). For instance, a result of Speiser states that the Riemann Hypothesis is is equivalent to ζ'(s) not vanishing in the region 0< Re(s) < 1/2. In this talk we will describe how the distribution of zeros of ζ'(s) relates to the distribution of the zeros of ζ(s) and survey some of the properties of the zeros of ζ'(s). We will also mention some recent progress on this problem.
Abstract: The talk will introduce the main ideas, old and present, in the theory of the representations of matrix groups over finite fields. We will focus on examples in order to introduce the main ideas of the general theory. This will include an overview, as well as a modest computation for the smallest case, of the Deligne-Lusztig characters, emphasising the strong connection between representation theory and algebraic geometry.
Contact me at: rudnick@post.tau.ac.il, Office : Schreiber 316, tel: 640-7806