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Julia Brandes
Senior Lecturer
Algebra and GeometryAbout 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.
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Two-dimensional Weyl sums failing square-root cancellation along
lines
Julia Brandes, Igor E. Shparlinski
Arkiv for Matematik - 2023 -
ON THE INHOMOGENEOUS VINOGRADOV
SYSTEM
Julia Brandes, K. Hughes
Bulletin of the Australian Mathematical Society - 2022 -
Optimal mean value estimates beyond Vinogradov's mean value
theorem
Julia Brandes, T. D. Wooley
Acta Arithmetica - 2021 -
Rational lines on cubic
hypersurfaces
Julia Brandes, R. Dietmann
Mathematical Proceedings of the Cambridge Philosophical Society - 2021 -
The density of rational lines on hypersurfaces: a bihomogeneous
perspective
Julia Brandes
Monatshefte für Mathematik - 2021 -
On generating functions in additive number theory, II: lower-order terms and applications to
PDEs
Julia Brandes, S. T. Parsell, C. Poulias, G. Shakan, R. C. Vaughan
Mathematische Annalen - 2021 -
On the number of linear spaces on hypersurfaces with a prescribed
discriminant
Julia Brandes
Mathematische Zeitschrift - 2018 -
Linear Spaces on Hypersurfaces over Number
Fields
Julia Brandes
The Michigan mathematical journal - 2017 -
Simultaneous additive equations: Repeated and differing
degrees
Julia Brandes, Scott T. Parsell
Canadian Journal of Mathematics - 2017 -
Vinogradov systems with a slice
off
Julia Brandes, Trevor Wooley
Mathematika - 2017 -
The Hasse Principle for Systems of Quadratic and Cubic Diagonal
Equations
Julia Brandes
Quarterly Journal of Mathematics - 2017 -
Forms representing forms: The definite
case
Julia Brandes
Journal of the London Mathematical Society - 2015 -
A note on p-adic solubility for forms in many
variables
Julia Brandes
Bulletin of the London Mathematical Society - 2015 -
Sums and differences of power-free
numbers
Julia Brandes
Acta Arithmetica - 2015 -
Forms representing forms and linear spaces on
hypersurfaces
Julia Brandes
Proceedings of the London Mathematical Society - 2014