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arXiv · 1410.7892

Kloosterman paths and the shape of exponential sums

Emmanuel Kowalski·William F. Sawin
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Abstract

We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums, as their parameter varies modulo a prime tending to infinity. Using independence of Kloosterman sheaves, we prove convergence in the sense of finite distributions to a specific random Fourier series. We also consider Birch sums, for which we can establish convergence in law in the space of continuous functions. We then derive some applications.

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Emmanuel Kowalski, William F. Sawin. 2014-10-29. Kloosterman paths and the shape of exponential sums. https://doi.org/10.1112/s0010437x16007351

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