Julia Brandes
My research interests lie in the area of analytic number theory, especially applications of the Hardy-Littlewood circle method. This is a Fourier-analytic method for estimating the number of solutions of diophantine equations which has been developed in the 1920s. But although the basic method is quite classical, its versatility makes it a strong tool that continues to yield new and exciting results. Furthermore, since polynomial equations occupy a central position in many fields of mathematics, results obtained by the circle method find applications in a wide range of problems.
Showing 13 publications
Campana Points on Diagonal Hypersurfaces
Local mean value estimates for Weyl sums
Two-dimensional Weyl sums failing square-root cancellation along lines
ON THE INHOMOGENEOUS VINOGRADOV SYSTEM
Optimal mean value estimates beyond Vinogradov's mean value theorem
The density of rational lines on hypersurfaces: a bihomogeneous perspective
On generating functions in additive number theory, II: lower-order terms and applications to PDEs
Rational lines on cubic hypersurfaces
On the number of linear spaces on hypersurfaces with a prescribed discriminant
Simultaneous Additive Equations: Repeated and Differing Degrees
Vinogradov systems with a slice off
Linear spaces on hypersurfaces over number fields
The Hasse Principle for Systems of Quadratic and Cubic Diagonal Equations
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Showing 1 research projects
Higher-dimensional structures on hypersurfaces