Colloquium: Cornelius Greither (Bundeswehr University Munich) — a short panoramic tour of some zeta functions

Thu, 21/01/202114:30-15:30
One might say that there exist zeta functions of three kinds: the very well-known ones (whose stock example is Riemann's zeta function); some less familiar ones; and at least one type which has been totally forgotten for decades. We intend to mention instances of all three types. The first type is important, if not predominant, in algebraic number theory, as we will try to illustrate by (very few) examples. As examples of the second type we will discuss zeta functions of finite groups. The third type refers to a class of zeta functions, attached to commutative rings, that was invented by Kähler. We will discuss it and the possible reasons why it has failed to catch on. All along we will try to
indicate what all zeta functions have in common. They measure something, e.g. probabilities in some sense, or they enumerate something, like ideals; these two aspects are related. Of course the
differences between the types will also be highlighted.