Brief history of results for irrationals
First considered by Hardy and Littlewood for
classical arithmetic functions which are connected
to degree 2 L-functions of automorphic forms on
from before or
d(n) = divisor function
Later results by Walfisz, Erdos, etc. are sharp, but
mainly apply to Eisenstein series.
No clean, uniform statement is possible in the
Eisenstein case because of large main terms,
which, however, are totally understood.