18 citations · 42 across the 19 of their papers we have counts for
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Two-dimensional Weyl sums failing square-root cancellation along lines
Julia Brandes, Igor E. Shparlinski
We show that a certain two-dimensional family of Weyl sums of length takes values as large as on almost all linear slices of the unit torus, contradicting a wi…
The density of rational lines on hypersurfaces: A bihomogeneous perspective
Julia Brandes
Let be a non-singular homogeneous polynomial of degree in variables. We give an asymptotic formula of the pairs of integer points with $|\mathb…
The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces
Julia Brandes, Scott T. Parsell
We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree and one general form of degree , where is smaller than . B…
On generating functions in additive number theory, II: Lower-order terms and applications to PDEs
Julia Brandes, Scott T. Parsell, Konstantinos Poulias +2
We obtain asymptotics for sums of the form involving lower order main terms. As an application, we show that for almost all one…