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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 Sawins work on Kloosterman paths.
Let $f(n)$ be a multiplicative function with $|f(n)|leq 1, q$ be a prime number and $a$ be an integer with $(a, q)=1, chi$ be a non-principal Dirichlet character modulo $q$. Let $varepsilon$ be a sufficiently small positive constant, $A$ be a large c
Given a finite set of integers $A$, its sumset is $A+A:= {a_i+a_j mid a_i,a_jin A}$. We examine $|A+A|$ as a random variable, where $Asubset I_n = [0,n-1]$, the set of integers from 0 to $n-1$, so that each element of $I_n$ is in $A$ with a fixed pro
We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.
Using $ell$-adic cohomology of tensor inductions of lisse $overline{mathbb Q}_ell$-sheaves, we study a class of incomplete character sums.
A $k$-sum of a set $Asubseteq mathbb{Z}$ is an integer that may be expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of the number of $(k+1)$-sums to the number of $k$-sums be? Writing $kwedge A$ for the set of $k$-sums of $