3 papers
math.NT2024
A lower bound on high moments of character sums
Barnabás Szabó
For any real and large prime , we prove a lower bound on the -th moment of the Dirichlet character sum \begin{equation*} \frac{1}{ϕ(q)} \sum_{\substack{χ\text{ mod…
math.NT2023
High moments of theta functions and character sums
Barnabás Szabó
Assuming the Generalised Riemann Hypothesis, we prove a sharp upper bound on moments of shifted Dirichlet -functions. We use this to obtain conditional upper bounds on high mome…
math.NT2022
On the existence of products of primes in arithmetic progressions
Barnabás Szabó
We study the existence of products of primes in arithmetic progressions, building on the work of Ramaré and Walker. One of our main results is that if is a large modulus, then…