Two Approaches to Compute Gl (3) Automorphic Forms: a Topic in Computational Number Theory

Ce Bian and Andrew Booker exhibited the first example of a third degree transcendental L-function at the American Institute of Mathematics (AIM). These L-functions encode deep underlying connections between many different areas of mathematics. While the result was announced the news caused excitement at the workshop attended by 25 of the world's leading analytic number theorists. "This breakthrough opens a door to the study of higher degree L-functions," said Dennis Hejhal, Professor of Mathematics at the University of Minnesota and Uppsala University. "It's a big advance" added Harold Stark of the University of California, San Diego, who, 30 years ago was the first to accurately calculate second degree transcendental L-functions. "I thought we were years away from doing this. The geometry of what you have to do and the scale of the computation are orders of magnitude harder." Dorian Goldfeld, Professor of Mathematics at Columbia University summarized the excitement, saying ``This discovery is analogous to finding planets in remote solar systems. We know they are out there, but the problem is to detect them and determine what they look like. It gives us a glimpse of new worlds"