Alexander Dunn

activity

20162026

most citedThe twisted second moment of modular half integral weight

L

--functions

4 citations · 5 across the 7 of their papers we have counts for

collaborators

12 papers

math.NT2026

Non-orthogonality of the cubic and quartic large sieves via Rankin-Selberg

Alexandre de Faveri, Alexander Dunn, Jeffrey Hoffstein

We show unconditionally that the cubic and quartic large sieves are not perfectly orthogonal. The main obstruction to perfect orthogonality comes from the bias exhibited by Gauss s…

math.NT2026

Non-vanishing for quartic Hecke $L$ -functions and ranks of elliptic curves

Cruz Castillo, Alexandre de Faveri, Alexander Dunn

We show that a positive proportion of Hecke $L$ -functions attached to the quartic residue symbols $(\frac{\cdot}{q})_{4}$ for squarefree $q \in Z [i]$ do not vanish…

math.NT2023

Quartic Gauss sums over primes and metaplectic theta functions

Chantal David, Alexander Dunn, Alia Hamieh +1

We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve ov…

math.NT2021★ 1 cited

Bias in cubic Gauss sums: Patterson's conjecture

Alexander Dunn, Maksym Radziwiłł

Let $W$ be a smooth test function with compact support in $(0, \infty)$ . Conditional on the Generalized Riemann Hypothesis for Hecke $L$ -functions over $Q (ω)$ , we prove tha…

math.NT2020

On a problem of Hoffstein and Kontorovich

Alexander Dunn

Let $π$ be a cuspidal automorphic representation of $GL_{2} (A_{Q})$ and $d$ be a fundamental discriminant. Hoffstein and Kontorovich ask for a bound…

math.NT2019

Bilinear forms in Weyl sums for modular square roots and applications

Alexander Dunn, Bryce Kerr, Igor E. Shparlinski +1

Let $q$ be a prime, $P \geq 1$ and let $N_{q} (P)$ denote the number of rational primes $p \leq P$ that split in the imaginary quadratic field $Q (- q)$ . The first part…

math.NT2019★ 4 cited

The twisted second moment of modular half integral weight $L$ --functions

Alexander Dunn, Alexandru Zaharescu

Given a half-integral weight holomorphic Kohnen newform $f$ on $Γ_{0} (4)$ , we prove an asymptotic formula for large primes $p$ with power saving error term for \begin{equation*} \sid…

math.NT2018

Maass forms and the mock theta function $f (q)$

Scott Ahlgren, Alexander Dunn

Let $f (q) = 1 + \sum_{n = 1}^{\infty} α (n) q^{n}$ be the well-known third order mock theta of Ramanujan. In 1964, George Andrews proved an asymptotic formula of the form $$α(n)= \sum_{c\leq…

math.NT2018

Sums of Kloosterman sums over primes in an arithmetic progression

Alexander Dunn, Alexandru Zaharescu

For $q$ prime, $X \geq 1$ and coprime $u, v \in N$ we estimate the sums \begin{equation*} \sum_{\substack{p \leq X \substack p \equiv u \hspace{-0.25cm} \mod{v} p \text{ pr…

math.NT2017

Uniform bounds for sums of Kloosterman sums of half integral weight

Alexander Dunn

For $m, n > 0$ and $mn < 0$ we estimate the sums \begin{equation*} \sum_{c \leq x} \frac{S(m,n,c,χ)}{c}, \end{equation*} where the $S (m, n, c, χ)$ are Kloosterman sums attached to a multip…

math.NT2017

Polynomial partition asymptotics

Alexander Dunn, Nicolas Robles

Let $f \in Z [y]$ be a polynomial such that $f (N) \subseteq N$ , and let $p_{A_{f}} (n)$ denote number of partitions of $n$ whose parts lie in the…

math.NT2016

On the distribution of $α p^{γ} + β$ modulo one

Alexander Dunn

Let $∥ \cdot ∥$ denote the minimum distance to an integer. For $0 < γ < 1$ , $θ > 0$ and $(α, β) \in R ∖ {0} \times R$ we study when \begin{equation*} \|αp^γ+…

Non-orthogonality of the cubic and quartic large sieves via Rankin-Selberg

Non-vanishing for quartic Hecke L-functions and ranks of elliptic curves

Quartic Gauss sums over primes and metaplectic theta functions

Bias in cubic Gauss sums: Patterson's conjecture

On a problem of Hoffstein and Kontorovich

Bilinear forms in Weyl sums for modular square roots and applications

The twisted second moment of modular half integral weight L--functions

Maass forms and the mock theta function f(q)

Sums of Kloosterman sums over primes in an arithmetic progression

Uniform bounds for sums of Kloosterman sums of half integral weight

Polynomial partition asymptotics

On the distribution of αpγ+β modulo one

Non-vanishing for quartic Hecke $L$ -functions and ranks of elliptic curves

The twisted second moment of modular half integral weight $L$ --functions

Maass forms and the mock theta function $f (q)$

On the distribution of $α p^{γ} + β$ modulo one