L-函数研究获得突破
(转自美国数学会网站)
Breakthrough in the Study of L-functions
On March 12, 2008, a new mathematical
object was revealed during a lecture at the American
Institute of Mathematics (AIM). Two researchers from the University of
Bristol exhibited the first example of a generic automorphic cusp form for the
general linear group of 3 by 3 matrices and its corresponding degree 3 L-function. These L-functions encode deep underlying connections between
many different areas of mathematics. The Riemann zeta function,
which is an L-function, is at the heart of the Riemann Hypothesis
(RH), one of the outstanding open problems in mathematics. RH should be true
for every L-function, not just the Riemann zeta function, and during the
workshop researchers made preliminary checks that the new L-function
satisfies RH. The new L-function was found by Andrew Booker
and his student Ce Bian and has generated excitement
among number theorists. "The numerical calculation done by Booker and Bian
is quite striking," said Peter Sarnak
of Princeton University
and the Institute for Advanced Study in Princeton.
"I had no idea that it would be feasible. This kind of number-theoretic
computation does not just involve using some faster available codes and then
number crunch. Rather it demands a deep mastery of the underlying mathematics
and then invention of fast techniques and algorithms."
相关报道Glimpses of a new (mathematical) world