arXiv subjects

David Lowry-Duda

Publications and source records attributed to David Lowry-Duda.

40 records · Page 3Linked to original sources

arXiv2016

On Functions Whose Mean Value Abscissas Are Midpoints, with Connections to Harmonic Functions

We investigate functions with the property that for every interval, the slope at the midpoint of the interval is the same as the average slope. More generally, we find functions whose average slopes over intervals are given by the slope at a weighted average of the endpoints of those intervals. This is equivalent to finding functions satisfying a weighted mean value property. In the course of our exploration, we find connections to harmonic functions that prompt us to explore multivariable analogues and the existence of "weighted harmonic functions."

math.CA↗

arXiv2016

Traces, high powers and one level density for families of curves over finite fields

The zeta function of a curve $C$ over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix $Θ_C$. We develop and present a new technique to compute the expected value of $\mathrm{Tr}(Θ_C^n)$ for various moduli spaces of curves of genus $g$ over a fixed finite field in the limit as $g$ is large, generalizing and extending the work of Rudnick and Chinis. This is achieved by using function field zeta functions, explicit formulae, and the densities of prime polynomials with prescribed ramification types at certain places as given by Bucur, David, Feigon, Kaplan, Lalín and Wood [BDF$^+$16] and by Zhao. We extend [BDF$^+$16] by describing explicit dependence on the place and give an explicit proof of the Lindelöf bound for function field Dirichlet $L$-functions $L(1/2 + it, χ)$. As applications, we compute the one-level density for hyperelliptic curves, cyclic $\ell$-covers, and cubic non-Galois covers.

math.NT↗

arXiv2016

Sign Changes of Coefficients and Sums of Coefficients of L-Functions

We extend the axiomatization for detecting and quantifying sign changes of Meher and Murty to sequences of complex numbers. We further generalize this result when the sequence is comprised of the coefficients of an $L$-function. As immediate applications, we prove that there are sign changes in intervals within sequences of coefficients of GL(2) holomorphic cusp forms, GL(2) Maass forms, and GL(3) Maass forms. Building on previous works by the authors, we prove that there are sign changes in intervals within sequences of partial sums of coefficients of GL(2) holomorphic cusp forms and Maass forms.

math.NT↗

arXiv2014

A Friendly Intro to Sieves with a Look Towards Recent Progress on the Twin Primes Conjecture

This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention several sieves, some with a lot of detail and some with very little detail. I also discuss several results and built upon many sources. I'll provide missing details and/or sources for additional reading here.

math.NT↗