368 AUDREY TERRAS, ARITHMETICAL QUANTUM CHAOS
Figure 7. Tessellation o f t h e 3-regular tree from K4Figure 8. Tessellation of H 49 from GL(2, IF7)Exercise 12. Show that if Z( u) is the Selberg zeta fimction in column 1 of Table 3,
then Z(s + l )/Z(s) has the same sort of prodilct formula as the !hara ze ta function
in column 2 of th e same table.
If you would like to read more about trace formulas on continuous sy mmetric
sp aces, some references are: Buse r [ 16 ], Elstrodt [25], Elstrodt, Grunewald and
Mennicke [ 26 ], Hejhal [ 36 ], Selberg [ 69 ] and Terras [ 83 ]. R eferences for the trace
formula on trees are: Ahumada [ 1 ], Nagoshi [ 63 ], Terras [ 82 ] and Venkov and
Nikit in [ 89 ]. A reference for t he trace formula on finite upper half pl a nes is Terras
[ 82 ].
- Pictures of Eigenfunctions
We will make only a few remarks here about the studies quantum ch aoticists make
of eige nfunctions of t heir favorite operators. T h e m ain problem here concerns t h e