Mathematical frontiersFirst example of a third degree transcendental L-function exhibited
“A glimpse of new worlds” — this is how Columbia University’s Dorian Goldfeld described the L-function breakthrough; L-functions hold most of the secrets of number theory, and now we are a step closer to lifting this veil of mystery
Readers of the Daily Wire would know that we often criticize the decline in the study of mathematics and engineering in American high school and colleges, and that we join many others in worrying about what this decline portends for the national security and welfare of the United States (see, for example, this recent HSDW story). What is especially frustrating is the fact that this decline is not the result of inexorable cultural tendencies but rather the outcome of misguided governmental budgetary and policy priorities, especially noticeable in the past seven years. Different priorities would have yielded different results. Criticism is not enough, though, so we want to make our own contribution to making busy and accomplished individuals — these are the two salient characteristics of our readers — aware of the latest developments in mathematics. Beginning today, we will periodically take our readers on a tour of the frontiers of mathematics.
A new mathematical object was revealed last week during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics. The news caused quite a stir at the AIM workshop attended by twenty-five of the world’s leading analytic number theorists. The work is a joint project between Ce Bian and his adviser, Andrew Booker. Booker commented that, “This work was made possible by a combination of theoretical advances and the power of modern computers.” During his lecture, Bian reported that it took approximately 10,000 hours of computer time to produce his initial results. “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, thirty 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.”
You may recall from Number Theory 101 that there are two types of L-functions: algebraic and transcendental, and these are classified according to their degree. The Riemann zeta-function may be described as the grand-daddy of all L-functions. It
