View the Riemann sphere as the boundary of hyperbolic
3-space 
,
and view 
as a group of isometries of .
Consider
,
the bottom of the spectrum of the
Laplacian 
on
(note the minus sign).
Except in trivial cases,
is a bona fide eigenvalue;
we call it the ``lowest eigenvalue'' of ,
or of .
Physically, it is the square of
the frequency of the the bass note of --the
lowest note you would hear if you hit
with a mallet.
We will prove the conjecture of Phillips and Sarnak
[13]
that for any classical Schottky group ,
where 
is some universal constant.