98-14 Marklof, Jens

Limit theorems for theta sums (66K, LATeX 2e/ams-LaTeX) Jan 12, 98

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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.

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