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 *L**L-function*s 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