random fourier series
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2016 ◽  
Vol 152 (7) ◽  
pp. 1489-1516 ◽  
Author(s):  
Emmanuel Kowalski ◽  
William F. Sawin

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.


2016 ◽  
Vol 23 (1) ◽  
pp. 207-228 ◽  
Author(s):  
Samuel Ronsin ◽  
Hermine Biermé ◽  
Lionel Moisan

2016 ◽  
Vol 44 (1) ◽  
pp. 684-738 ◽  
Author(s):  
Peter K. Friz ◽  
Benjamin Gess ◽  
Archil Gulisashvili ◽  
Sebastian Riedel

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