Allysa Lumley

activity

20182021

collaborators

5 papers

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

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

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

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…

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

Explicit zero density for the Riemann zeta function

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

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