Marklof, Jens
Limit theorems for theta sums
(66K, LATeX 2e/ams-LaTeX)
ABSTRACT. For almost all values of $x\in\RR$, the classical theta sum
$$ S_N(x)=N^{-1/2}\sum_{n=1}^N \e^{2\pi i n^2 x} $$ exhibits an
extremely irregular behaviour, as $N$ tends to infinity.
This limit is investigated by exploiting a connection
to the ergodic properties of flows on
the unit tangent bundle of a surface of constant
negative curvature.