6 citations · 10 across the 3 of their papers we have counts for
9 papers
Arithmetic Progressions of Squares and Multiple Dirichlet Series
Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1
We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic conti…
Triple Correlation Sums of Coefficients of Cusp Forms
Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1
We produce nontrivial asymptotic estimates for shifted sums of the form , in which are un-normalized Fourier coefficients of holomorphic cusp…
A Shifted Sum for the Congruent Number Problem
Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1
We introduce a shifted convolution sum that is parametrized by the squarefree natural number . The asymptotic growth of this series depends explicitly on whether or not is a…
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 between the area of a circle of radius and the number of lattice points it contains. In this paper, we study th…
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 , where is the discrepa…
Sign Changes of Coefficients and Sums of Coefficients of L-Functions
Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1
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 c…