Abstract: Since their first appearance in the work of Euler, L-functions have been some of the most important objects in modern number theory. They allow us to shift classical number-theoretical problems like „How many primes are there with some property P?“ or „How many rational points are there on an elliptic curve?“ into the realm of analysis, where there is usually a better chance of solving them.
During the 1970s a vast web of conjectures around these functions, called the Langlands program, was formulated. Its goal is to unify the different theories of L-functions and prove many of their useful properties. In this talk I try to give a „Big Picture“ overview of how L-functions arise in number theory, why they are useful and the role of the Langlands program in their exploration.
Special values of L-functions
16.12.2021 14:00 - 14:45
Organiser:
Vienna School of Mathematics
Location:
Big Blue Button