Speaker
David Broadhurst
Description
The on-shell equal-mass sunrise diagram with N-2 loops in two space-time dimensions
is an integral of a product of N Bessel functions. Using Schwinger parameters
one may try to guess modular forms that prevent reduction
to polylogarithms for N>4. I was able to do so for N=5,6 and 8,
obtaining evaluations of integrals of N Bessel functions
in terms of L-series of modular forms with weight N-2.
The case N=7 proved harder, but was conquered last week, thanks
to work by Ronald Evans, on Kloosterman sums, and an inspired
suggestion for the functional equation of the corresponding L-series,
from Anton Mellit.
