## Conference "Zeta Functions"## June 21 - 25, 2010## Moscow, Russia |

**Organisers:** Michel Balazard *(CNRS, Laboratoire Poncelet)*, Michael Tsfasman *(CNRS, Laboratoire Poncelet, Institute for Information Transmission Problems)*, Alexey Zykin *(Laboratoire Poncelet, State University Higher School of Economics)*

Tuesday 22 June, 16:30 - 17:30

One of the big questions in the area of curves over finite fields concerns the distribution of the numbers of points: Which numbers are possible as the number of points on a curve of genus $g$? The same question applies to various subclasses of curves. In this talk we classify the possibilities for the number of points on genus 4 hyperelliptic supersingular curves over finite fields of order $2^n$, $n$ odd.