Zeta function(s): A Perspective

Kirti Joshi

Since the work of Euler and Riemann, the Riemann Zeta function has
played an important role in number theory. Over the past hundred years
we have gleaned that the Riemann Zeta functions holds within it the
key to many mysteries of prime numbers. At the turn of the century
other zeta functions were introduced which brought with them secrets
from the realms of elliptic curves, abelian varieties, algebraic
cycles....and many other realms which have perhaps not been named or
identified.

In this introductory sequence of lectures, I will discuss some of the
Zeta functions which arise in number theory and also in many other
contexts and discuss the significance of the information these
functions encodes, and discuss many worked examples.