Allysa Lumley

activity

20142025

most citedShort effective intervals containing primes

14 citations · 29 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2025

Linear Combinations of Logarithms of $L$ -functions over Function Fields at Microscopic Shifts and Beyond

Fatma Çiçek, Pranendu Darbar, Allysa Lumley

In the function field setting with a fixed characteristic, it was proven by the second and third authors that the values $lo g L (\frac{1}{2}, χ_{D})$ as $D$ varies over…

math.NT2023

Asymmetric Distribution of Extreme Values of Cubic $L$ -functions at $s = 1$

Pranendu Darbar, Chantal David, Matilde Lalin +1

We investigate the distribution of values of cubic Dirichlet $L$ -functions at $s = 1$ . Following ideas of Granville and Soundararajan for quadratic $L$ -functions, we model the distri…

math.NT2021

Selberg's Central limit theorem for quadratic Dirichlet L-functions over function fields

Pranendu Darbar, Allysa Lumley

In this article, we study the logarithm of the central value $L (\frac{1}{2}, χ_{D})$ in the symplectic family of Dirichlet $L$ -functions associated with the hyperelliptic…

math.NT2021

Explicit zero density for the Riemann zeta function

Habiba Kadiri, Allysa Lumley, Nathan Ng

Let $N (σ, T)$ denote the number of nontrivial zeros of the Riemann zeta function with real part greater than $σ$ and imaginary part between $0$ and $T$ . We provide explicit upper bo…

math.NT2020

Primes in short intervals: Heuristics and calculations

Andrew Granville, Allysa Lumley

We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length $y$ around $x$ , where $y ≪ (lo g x)^{2}$ . In particular we…

math.NT2020

Sharper Bounds for the Chebyshev function $θ (x)$

Samuel Broadbent, Habiba Kadiri, Allysa Lumley +2

In this article, we provide explicit bounds for the prime counting function $θ (x)$ in all ranges of $x$ . The bounds for the error term for $θ (x) - x$ are of the shape $ε x$ and $\fra…

math.NT2018★ 5 cited

Explicit Bounds for $L$ -Functions on the Edge of the Critical Strip

Allysa Lumley

Assuming GRH and the Ramanujan-Petersson conjecture we prove explicit bounds for $L (1, f)$ for a large class of $L$ -functions $L (s, f)$ , which includes $L$ -functions attached to auto…

math.NT2018★ 10 cited

Complex Moments and the distribution of Values of $L (1, χ_{D})$ over Function Fields with Applications to Class Numbers

Allysa Lumley

In this paper we investigate the moments and the distribution of $L (1, χ_{D})$ , where $χ_{D}$ varies over quadratic characters associated to square-free polynomials $D$ of degree $n$ ov…

math.NT2014★ 14 cited

Short effective intervals containing primes

Habiba Kadiri, Allysa Lumley

We prove that if $x$ is large enough, namely $x \geq x_{0}$ , then there exists a prime between $x (1 - Δ^{- 1})$ and $x$ , where $Δ$ is an effective constant computed in terms of $x_{0}$ . Th…

Linear Combinations of Logarithms of L-functions over Function Fields at Microscopic Shifts and Beyond

Asymmetric Distribution of Extreme Values of Cubic L-functions at s=1

Selberg's Central limit theorem for quadratic Dirichlet L-functions over function fields

Explicit zero density for the Riemann zeta function

Primes in short intervals: Heuristics and calculations

Sharper Bounds for the Chebyshev function θ(x)

Explicit Bounds for L-Functions on the Edge of the Critical Strip

Complex Moments and the distribution of Values of L(1,χD​) over Function Fields with Applications to Class Numbers

Short effective intervals containing primes

Linear Combinations of Logarithms of $L$ -functions over Function Fields at Microscopic Shifts and Beyond

Asymmetric Distribution of Extreme Values of Cubic $L$ -functions at $s = 1$

Sharper Bounds for the Chebyshev function $θ (x)$

Explicit Bounds for $L$ -Functions on the Edge of the Critical Strip

Complex Moments and the distribution of Values of $L (1, χ_{D})$ over Function Fields with Applications to Class Numbers