Youness Lamzouri

activity

20242026

collaborators

11 papers

math.NT2026

A note on large values of Dirichlet $L$ -functions for characters of fixed order at $1/2 < I ¨ \leq 1$

Youness Lamzouri

In this note, we use a simple argument to show the existence of large values of conjecturally sharp size for Dirichlet $L$ -functions attached to primitive characters of fixed order…

math.NT2026

An omega result for the least negative Hecke eigenvalue

Youness Lamzouri

We establish the existence of many holomorphic Hecke eigenforms $f$ of large weight $k$ for the full modular group, for which the least positive integer $n_{f}$ such that $Î»_f(n_f)<…

math.NT2026

Sharp omega results for the divisor and circle problems

Youness Lamzouri

We establish omega results for the divisor and circle problems that are conjecturally sharp, while also determining the sign of the large values obtained. This improves on the work…

math.NT2026

Large values of exponential sums with multiplicative coefficients

Andrew Granville, Youness Lamzouri

In 1977 Montgomery and Vaughan gave tight bounds for exponential sums of the form $\sum_{n \leq x} f (n) e (n I^\pm)$ where $f$ is a $1$ -bounded multiplicative function and $I^\pm \in R$ …

math.NT2025

ErdÅs's integer dilation approximation problem and GCD graphs

Dimitris Koukoulopoulos, Youness Lamzouri, Jared Duker Lichtman

Let $A \subset R_{⩾ 1}$ be a countable set such that $lim sup_{x \to \infty} \frac{1}{l o g x} \sum_{I^\pm \in A \cap [1, x]} \frac{1}{I ^} \pm > 0$ . We prove that, for…

math.NT2024

The distribution of the maximum of cubic character sums

Youness Lamzouri, Kunjakanan Nath

For a primitive Dirichlet character $χ (mod q)$ we let \[M(χ):= \frac{1}{\sqrt{q}}\max_{1\leq t \leq q} \Big|\sum_{n \leq t} χ(n) \Big|.\] In this paper, we investigate the distribu…

A note on large values of Dirichlet L-functions for characters of fixed order at 1/2<I¨≤1

An omega result for the least negative Hecke eigenvalue

Sharp omega results for the divisor and circle problems

Large values of exponential sums with multiplicative coefficients

ErdÅs's integer dilation approximation problem and GCD graphs

The distribution of the maximum of cubic character sums

A note on large values of Dirichlet $L$ -functions for characters of fixed order at $1/2 < I ¨ \leq 1$

ErdÅs's integer dilation approximation problem and GCD graphs