The Limiting Distribution of Character Sums

@article{Hussain2021TheLD,
  title={The Limiting Distribution of Character Sums},
  author={Ayesha Hussain},
  journal={International Mathematics Research Notices},
  year={2021}
}
  • Ayesha Hussain
  • Published 14 October 2020
  • Mathematics
  • International Mathematics Research Notices
In this paper, we consider the distribution of the continuous paths of Dirichlet character sums modulo prime $q$ on the complex plane. We also find a limiting distribution as $q \rightarrow \infty $ using Steinhaus random multiplicative functions, stating properties of this random process. This is motivated by Kowalski and Sawin’s work on Kloosterman paths. 

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References

SHOWING 1-10 OF 27 REFERENCES
The distribution of the maximum of character sums
We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of characterExpand
Convergence of Probability Measures
MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS
We determine the order of magnitude of $\mathbb{E}|\sum _{n\leqslant x}f(n)|^{2q}$, where $f(n)$ is a Steinhaus or Rademacher random multiplicative function, and $0\leqslant q\leqslant 1$. In theExpand
On the support of the Kloosterman paths
We obtain statistical results on the possible distribution of all partial sums of a Kloosterman sum modulo a prime, by computing explicitly the support of the limiting random Fourier series of ourExpand
The Moment Problem
Kloosterman paths and the shape of exponential sums
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.Expand
Probability A Graduate Course
TLDR
The probability a graduate course is universally compatible with any devices to read, allowing you to get the most less latency time to download any of the authors' books like this one. Expand
The frequency and the structure of large character sums
Let $M(\chi)$ denote the maximum of $|\sum_{n\le N}\chi(n)|$ for a given non-principal Dirichlet character $\chi \pmod q$, and let $N_\chi$ denote a point at which the maximum is attained. In thisExpand
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