1 results
Kloosterman paths and the shape of exponential sums
- Part of
-
- Journal:
- Compositio Mathematica / Volume 152 / Issue 7 / July 2016
- Published online by Cambridge University Press:
- 15 April 2016, pp. 1489-1516
- Print publication:
- July 2016
-
- Article
-
- You have access
- Export citation
-
We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums
$\text{Kl}_{p}(a)$, as 
$a$ varies over 
$\mathbf{F}_{p}^{\times }$ and as 
$p$ tends 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.
