David Lowry-Duda

activity

20142026

most citedSecond Moments in the Generalized Gauss Circle Problem

21 citations · 125 across the 34 of their papers we have counts for

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Showing 2017 · math.NTShow all

5 papers · 2 filters

math.NT2017★ 5 cited

Uniform bounds for lattice point counting and partial sums of zeta functions

David Lowry-Duda, Takashi Taniguchi, Frank Thorne

We prove uniform versions of two classical results in analytic number theory. The first is an asymptotic for the number of points of a complete lattice $Λ \subseteq R^{d}$ in…

math.NT2017★ 3 cited

A Short Note on Gaps between Powers of Consecutive Primes

David Lowry-Duda

Let $α, β \geq 0$ and $α + β < 1$ . In this short note, we show that $lim inf_{n \to \infty} p_{n}^{β} (p_{n + 1}^{α} - p_{n}^{α}) = 0$ , where $p_{n}$ is the $n$ th prime. This notes an improvement ove…

math.NT2017★ 7 cited

On Some Variants of the Gauss Circle Problem

David Lowry-Duda

The Gauss Circle Problem concerns finding asymptotics for the number of lattice point lying inside a circle in terms of the radius of the circle. The heuristic that the number of p…

math.NT2017★ 4 cited

The Laplace Transform of the Second Moment in the Gauss Circle Problem

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

The Gauss circle problem concerns the difference $P_{2} (n)$ between the area of a circle of radius $n$ and the number of lattice points it contains. In this paper, we study th…

math.NT2017★ 21 cited

Second Moments in the Generalized Gauss Circle Problem

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_{k} (n)^{2}$ , where $P_{k} (n)$ is the discrepa…