Joshua Stucky

activity

20202024

collaborators

7 papers

math.NT2024

Non-vanishing for cubic Hecke $L$ -functions

Chantal David, Alexandre de Faveri, Alexander Dunn +1

Let $ω$ be a primitive cubic root of unity. We study the non-vanishing problem for the family of Hecke $L$ -functions associated to primitive cubic characters defined over the Eisen…

math.NT2024

The fourth moment of quadratic Dirichlet $L$ -Functions II

Quanli Shen, Joshua Stucky

We prove an asymptotic formula with four main terms for the fourth moment of quadratic Dirichlet $L$ -functions unconditionally. Our proof is based on the work of Li , Soundararajan…

math.NT2024

The distribution of $g cd (n, ϕ (n))$

Joshua Stucky

Let $ϕ (n)$ denote Euler's phi function. We study the distribution of the numbers $g c d (n, ϕ (n))$ and their divisors. Our results generalize previous results of Erdős and Pollack.

math.NT2022

Certain floor function sums over powers

Joshua Stucky

We study the sums $S_{f} (x) = n \leq x \sum f (⌊ \frac{x}{n} ⌋)$ when $f$ is supported on $r$ th powers with $r \geq 2$ . This restriction allows us…

math.NT2021

The sixth moment of automorphic $L$ -functions

Joshua Stucky

We investigate the sixth moment of the family of $L$ -functions associated to holomorphic modular forms on $G L_{2}$ with respect to a congruence subgroup $Γ_{1} (q)$ . We improve on previ…

math.NT2021

The fractional sum of small arithmetic functions

Joshua Stucky

Motivated by recent results, we study sums of the form $S_{f} (x) = \sum_{n \leq x} f (⌊ \frac{x}{n} ⌋)$ , where $f$ is an arithmetic function and $\left…

math.NT2020

Gaussian Primes in Narrow Sectors

Joshua Stucky

We generalize a Theorem of Ricci and count Gaussian primes $p$ with short interval restrictions on both the norm and the argument of $p$ .

Non-vanishing for cubic Hecke L-functions

The fourth moment of quadratic Dirichlet L-Functions II

The distribution of gcd(n,ϕ(n))

Certain floor function sums over powers

The sixth moment of automorphic L-functions

The fractional sum of small arithmetic functions

Gaussian Primes in Narrow Sectors

Non-vanishing for cubic Hecke $L$ -functions

The fourth moment of quadratic Dirichlet $L$ -Functions II

The distribution of $g cd (n, ϕ (n))$

The sixth moment of automorphic $L$ -functions