Lattice Green's Functions of the HigherDimensional FaceCentered Cubic Lattices
(by Christoph Koutschan)
On this webpage we give supplementary material which accompanies our article
Lattice Green's Functions of the HigherDimensional FaceCentered Cubic Lattices.
In particular, we provide a Mathematica notebook

fcc.nb (Mathematica 7.0 notebook, 189 kB)

fcc.nb.pdf (pdf screenshot of the notebook (if you don't have Mathematica), 319 kB)
containing all computations that are necessary to show that our
theorems are correct. Some certificates (those that take more than
just a few minutes to be computed  the others are directly computed
in the notebook) are given here:

The certificates for the 5D fcc lattice (Theorem 3):
fcc5_cert.zip (548 kB)

The certificates for the 6D fcc lattice (Theorem 5):
fcc6_cert.zip (14 MB)
Unzip these files and make sure that the data files fcc5_cert.m and
fcc6_cert.m are stored in a directory such that Mathematica can find
them. They will be loaded at the appropriate positions in the
notebook.
Additional packages that are needed for these computations and
verifications are
Asymptotics
and
HolonomicFunctions.
If you are only interested in the differential equations and
believe them without checking the proof, you can download
them here:
 The ODE for the LGF of the 4D fcc lattice: fcc4_de.m
 The ODE for the LGF of the 5D fcc lattice: fcc5_de.m
 The ODE for the LGF of the 6D fcc lattice: fcc6_de.m